<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="11" minor="0"/>
<Label-Scheme value="2" prefix=""/>
<View-Properties presentation="false"></View-Properties>
<MapleNet-Properties warnlevel="3" longdelim="true" plotoptions="" echo="1" errorcursor="false" elisiontermsthreshold="10000" elisiontermsbefore="100" errorbreak="1" prettyprint="3" prompt="&gt; " latexwidth="6.0" useclientjvm="true" ansi="false" screenheight="25" labelwidth="20" plotdevice="inline" typesetting="standard" displayprecision="-1" indentamount="4" elisiondigitsthreshold="10000" quiet="false" plotoutput="terminal" rtablesize="10" preplot="" showassumed="1" plotdriver="openviz" elisiontermsafter="100" labelling="true" postplot="" screenwidth="79" elisiondigitsbefore="100" elisiondigitsafter="100" verboseproc="1" imaginaryunit="I" ShowLabels="true"/>
<Styles><Font name="Maple Output12" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 4" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 1" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Left Justified Maple Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="9" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Variable" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Diagnostic" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[64,128,64]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Bold" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Page Number" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math Italic Small" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="1" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 3" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Nonterminal" background="[255,255,255]" bold="true" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Default" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Normal" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Comment" background="[255,255,255]" bold="true" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input" background="[255,255,255]" bold="true" executable="true" family="Monospaced" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math Small" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="1" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Inert Output" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[144,144,144]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Fixed" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 3" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Popup" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,128,128]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Plot Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Input" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Copyright" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input Placeholder" background="[255,255,255]" bold="true" executable="true" family="Monospaced" foreground="[200,0,200]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="true"/>
<Font name="2D Math Bold Small" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="1" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Fixed Width" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Error" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[255,0,255]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 1" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Notes" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Help Underlined Bold" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,128,128]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="2D Math Symbol 2" background="[255,255,255]" bold="false" executable="false" family="SymbolPi" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Normal256" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 5" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text Output" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Bullet Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Equation Label" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Author" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 2" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="14" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Plot Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="8" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Plot" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Italic" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Heading" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="14" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Output Labels" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="8" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Normal" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Comment" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Maple Name" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[104,64,92]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,255]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Dictionary Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[147,0,15]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Help Emphasized" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Italic Bold" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="LaTeX" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Menus" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Dash Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 4" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Prompt" background="[255,255,255]" bold="true" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Underlined" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Line Printed Output" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="List Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Underlined Italic" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Warning" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math Bold" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math Italic" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 2" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Layout name="Maple Output12" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.5" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Normal256" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 4" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 5" alignment="left" bullet="ROMAN" firstindent="0" leftmargin="144" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 1" alignment="left" bullet="numeric" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Text Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Left Justified Maple Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.5" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Bullet Item" alignment="left" bullet="dot" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Help" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Author" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="8" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Diagnostic" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 2" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="2" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 3" alignment="left" bullet="roman" firstindent="0" leftmargin="72" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Maple Plot" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Normal" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Annotation Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Dash Item" alignment="left" bullet="dash" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 3" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 4" alignment="left" bullet="ALPHABETIC" firstindent="0" leftmargin="108" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Maple Output" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.5" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="List Item" alignment="left" bullet="indent" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Line Printed Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Fixed Width" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Warning" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Error" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 1" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="4" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 2" alignment="left" bullet="alphabetic" firstindent="0" leftmargin="36" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Pencil-style name="Pencil 3" pen-color="[0,0,0]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 1" pen-color="[0,0,0]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 5" pen-color="[255,0,0]" pen-height="5.0" pen-width="5.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 2" pen-color="[0,0,255]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 4" pen-color="[0,0,255]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Highlighter-style name="Highlighter 2" pen-color="[255,204,0]" pen-height="14.0" pen-width="14.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 4" pen-color="[0,255,255]" pen-height="32.0" pen-width="32.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 3" pen-color="[51,255,0]" pen-height="24.0" pen-width="24.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 1" pen-color="[255,153,255]" pen-height="12.0" pen-width="8.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 5" pen-color="[255,255,0]" pen-height="48.0" pen-width="48.0" pen-opacity="0.8"/>
</Styles>
<Page-Numbers enabled="false" first-number="1" first-numbered-page="1" horizontal-location="right" style="Page Number" vertical-location="bottom"/>
<Task-table>
    <Task-category name="&lt;default&gt;">
    </Task-category>
</Task-table>
<Annotation-table>
    <Annotation-category name="&lt;default&gt;">
    </Annotation-category>
</Annotation-table>
<Task>
</Task>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 2.3.14  Graetz Problem - Finite Difference Solution</Font></Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
</Group>
<Group labelreference="L3" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTkc2IiIjPw==">IiM/</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">L:=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTEc2IiIiIg==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=diff(y(x),x$2)+1/x*diff(y(x),x)+lambda^2*(1-x^2)*y(x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIsKC1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ5R0YkNiNJInhHRiQtSSIkR0YoNiRGLSIiIyIiIiomRi0hIiItRic2JEYqRi1GMkYyKigpSSdsYW1iZGFHRiRGMUYyLCZGMkYyKiQpRi1GMUYyRjRGMkYqRjJGMg==">LCgtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYkNiQtSSJ5RzYiNiNJInhHRitGLUYtIiIiKiZGLSEiIkYnRi5GLiooKUknbGFtYmRhR0YrIiIjRi4sJkYuRi4qJClGLUY0Ri5GMEYuRilGLkYu</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=diff(y(x),x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiQ2I0kieEdGJEYs">LUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHNiI2I0kieEdGKEYq</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=y(x)-0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLUkieUdGJDYjSSJ4R0Yk">LUkieUc2IjYjSSJ4R0Yk</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The additional boundary condition is entered here:</Text-field>
</Input>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc3:=y(x)-1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMzRzYiLCYtSSJ5R0YkNiNJInhHRiQiIiJGKiEiIg==">LCYtSSJ5RzYiNiNJInhHRiUiIiJGKCEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The central difference expressions for the second and first derivatives are</Text-field>
</Input>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">d2ydx2:=(y[m+1]-2*y[m]+y[m-1])/h^2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknZDJ5ZHgyRzYiKiYsKCZJInlHRiQ2IywmSSJtR0YkIiIiRixGLEYsKiYiIiNGLCZGKDYjRitGLCEiIiZGKDYjLCZGK0YsRixGMUYsRiwpSSJoR0YkRi5GMQ==">KiYsKCZJInlHNiI2IywmSSJtR0YmIiIiRipGKkYqKiYiIiNGKiZGJTYjRilGKiEiIiZGJTYjLCZGKUYqRipGL0YqRiopSSJoR0YmRixGLw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydx:=(y[m+1]-y[m-1])/2/h;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklZHlkeEc2IiwkKigjIiIiIiIjRigsJiZJInlHRiQ2IywmSSJtR0YkRihGKEYoRigmRiw2IywmRi9GKEYoISIiRjNGKEkiaEdGJEYzRig=">LCQqKCMiIiIiIiNGJSwmJkkieUc2IjYjLCZJIm1HRipGJUYlRiVGJSZGKTYjLCZGLUYlRiUhIiJGMUYlSSJoR0YqRjFGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> Three point forward and backward difference expressions for the derivative are:</Text-field>
</Input>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxf:=(-y[2]+4*y[1]-3*y[0])/(2*h);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGZHNiIsJCooIyIiIiIiI0YoLCgmSSJ5R0YkNiNGKSEiIiomIiIlRigmRiw2I0YoRihGKComIiIkRigmRiw2IyIiIUYoRi5GKEkiaEdGJEYuRig=">LCQqKCMiIiIiIiNGJSwoJkkieUc2IjYjRiYhIiIqJiIiJUYlJkYpNiNGJUYlRiUqJiIiJEYlJkYpNiMiIiFGJUYsRiVJImhHRipGLEYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxb:=(y[N-1]-4*y[N]+3*y[N+1])/(2*h);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGJHNiIsJCooIyIiIiIiI0YoLCgmSSJ5R0YkNiMiIz5GKComIiIlRigmRiw2IyIjP0YoISIiKiYiIiRGKCZGLDYjIiNARihGKEYoSSJoR0YkRjRGKA==">LCQqKCMiIiIiIiNGJSwoJkkieUc2IjYjIiM+RiUqJiIiJUYlJkYpNiMiIz9GJSEiIiomIiIkRiUmRik2IyIjQEYlRiVGJUkiaEdGKkYyRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> The governing equation in finite difference form is:</Text-field>
</Input>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq[m]:=subs(diff(y(x),x$2)=d2ydx2,diff(y(x),x)=dydx,y(x)=y[m],x=m*h,eq);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiNJIm1HRiUsKComLCgmSSJ5R0YlNiMsJkYnIiIiRi9GL0YvKiYiIiNGLyZGLEYmRi8hIiImRiw2IywmRidGL0YvRjNGL0YvKUkiaEdGJUYxRjNGLyoqI0YvRjFGL0YnRjNGN0YzLCZGK0YvRjRGM0YvRi8qKClJJ2xhbWJkYUdGJUYxRi8sJkYvRi8qJilGJ0YxRi9GN0YvRjNGL0YyRi9GLw==">LCgqJiwoJkkieUc2IjYjLCZJIm1HRiciIiJGK0YrRisqJiIiI0YrJkYmNiNGKkYrISIiJkYmNiMsJkYqRitGK0YwRitGKylJImhHRidGLUYwRisqKiNGK0YtRitGKkYwRjRGMCwmRiVGK0YxRjBGK0YrKigpSSdsYW1iZGFHRidGLUYrLCZGK0YrKiYpRipGLUYrRjRGK0YwRitGLkYrRis=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> The boundary conditions in finite difference form are:</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq[0]:=subs(diff(y(x),x)=dydxf,y(x)=y[0],bc1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiEsJCooIyIiIiIiI0YrLCgmSSJ5R0YlNiNGLCEiIiomIiIlRismRi82I0YrRitGKyomIiIkRismRi9GJkYrRjFGK0kiaEdGJUYxRis=">LCQqKCMiIiIiIiNGJSwoJkkieUc2IjYjRiYhIiIqJiIiJUYlJkYpNiNGJUYlRiUqJiIiJEYlJkYpNiMiIiFGJUYsRiVJImhHRipGLEYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq[N+1]:=subs(diff(y(x),x)=dydxb,y(x)=y[N+1],bc2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiI0AmSSJ5R0YlRiY=">JkkieUc2IjYjIiNA</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> A 'for loop' can be written for the interior node points as</Text-field>
</Input>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do Eq[i]:=subs(m=i,Eq[m]);od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiIsKComLCgmSSJ5R0YlNiMiIiNGJyomRi5GJyZGLEYmRichIiImRiw2IyIiIUYnRicpSSJoR0YlRi5GMUYnKigjRidGLkYnRjVGMSwmRitGJ0YyRjFGJ0YnKigpSSdsYW1iZGFHRiVGLkYnLCZGJ0YnKiRGNUYnRjFGJ0YwRidGJw==">LCgqJiwoJkkieUc2IjYjIiIjIiIiKiZGKUYqJkYmNiNGKkYqISIiJkYmNiMiIiFGKkYqKUkiaEdGJ0YpRi5GKiooI0YqRilGKkYyRi4sJkYlRipGL0YuRipGKiooKUknbGFtYmRhR0YnRilGKiwmRipGKiokRjJGKkYuRipGLEYqRio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiMsKComLCgmSSJ5R0YlNiMiIiQiIiIqJkYnRi8mRixGJkYvISIiJkYsNiNGL0YvRi8pSSJoR0YlRidGMkYvKigjRi8iIiVGL0Y1RjIsJkYrRi9GM0YyRi9GLyooKUknbGFtYmRhR0YlRidGLywmRi9GLyomRjlGL0Y1Ri9GMkYvRjFGL0Yv">LCgqJiwoJkkieUc2IjYjIiIkIiIiKiYiIiNGKiZGJjYjRixGKiEiIiZGJjYjRipGKkYqKUkiaEdGJ0YsRi9GKiooI0YqIiIlRipGMkYvLCZGJUYqRjBGL0YqRioqKClJJ2xhbWJkYUdGJ0YsRiosJkYqRioqJkY2RipGMkYqRi9GKkYtRipGKg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiQsKComLCgmSSJ5R0YlNiMiIiUiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjRjFGL0YvKUkiaEdGJUYxRjNGLyooI0YvIiInRi9GNkYzLCZGK0YvRjRGM0YvRi8qKClJJ2xhbWJkYUdGJUYxRi8sJkYvRi8qJiIiKkYvRjZGL0YzRi9GMkYvRi8=">LCgqJiwoJkkieUc2IjYjIiIlIiIiKiYiIiNGKiZGJjYjIiIkRiohIiImRiY2I0YsRipGKilJImhHRidGLEYwRioqKCNGKiIiJ0YqRjNGMCwmRiVGKkYxRjBGKkYqKigpSSdsYW1iZGFHRidGLEYqLCZGKkYqKiYiIipGKkYzRipGMEYqRi1GKkYq</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiUsKComLCgmSSJ5R0YlNiMiIiYiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiIkRi9GLylJImhHRiVGMUYzRi8qKCNGLyIiKUYvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiIztGL0Y3Ri9GM0YvRjJGL0Yv">LCgqJiwoJkkieUc2IjYjIiImIiIiKiYiIiNGKiZGJjYjIiIlRiohIiImRiY2IyIiJEYqRiopSSJoR0YnRixGMEYqKigjRioiIilGKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiM7RipGNEYqRjBGKkYtRipGKg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiYsKComLCgmSSJ5R0YlNiMiIiciIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiIlRi9GLylJImhHRiVGMUYzRi8qKCNGLyIjNUYvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiI0RGL0Y3Ri9GM0YvRjJGL0Yv">LCgqJiwoJkkieUc2IjYjIiInIiIiKiYiIiNGKiZGJjYjIiImRiohIiImRiY2IyIiJUYqRiopSSJoR0YnRixGMEYqKigjRioiIzVGKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiNERipGNEYqRjBGKkYtRipGKg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIicsKComLCgmSSJ5R0YlNiMiIigiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiImRi9GLylJImhHRiVGMUYzRi8qKCNGLyIjN0YvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiI09GL0Y3Ri9GM0YvRjJGL0Yv">LCgqJiwoJkkieUc2IjYjIiIoIiIiKiYiIiNGKiZGJjYjIiInRiohIiImRiY2IyIiJkYqRiopSSJoR0YnRixGMEYqKigjRioiIzdGKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiNPRipGNEYqRjBGKkYtRipGKg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIigsKComLCgmSSJ5R0YlNiMiIikiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiInRi9GLylJImhHRiVGMUYzRi8qKCNGLyIjOUYvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiI1xGL0Y3Ri9GM0YvRjJGL0Yv">LCgqJiwoJkkieUc2IjYjIiIpIiIiKiYiIiNGKiZGJjYjIiIoRiohIiImRiY2IyIiJ0YqRiopSSJoR0YnRixGMEYqKigjRioiIzlGKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiNcRipGNEYqRjBGKkYtRipGKg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiksKComLCgmSSJ5R0YlNiMiIioiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiIoRi9GLylJImhHRiVGMUYzRi8qKCNGLyIjO0YvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiI2tGL0Y3Ri9GM0YvRjJGL0Yv">LCgqJiwoJkkieUc2IjYjIiIqIiIiKiYiIiNGKiZGJjYjIiIpRiohIiImRiY2IyIiKEYqRiopSSJoR0YnRixGMEYqKigjRioiIztGKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiNrRipGNEYqRjBGKkYtRipGKg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiosKComLCgmSSJ5R0YlNiMiIzUiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiIpRi9GLylJImhHRiVGMUYzRi8qKCNGLyIjPUYvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiIyIpRi9GN0YvRjNGL0YyRi9GLw==">LCgqJiwoJkkieUc2IjYjIiM1IiIiKiYiIiNGKiZGJjYjIiIqRiohIiImRiY2IyIiKUYqRiopSSJoR0YnRixGMEYqKigjRioiIz1GKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiMiKUYqRjRGKkYwRipGLUYqRio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzUsKComLCgmSSJ5R0YlNiMiIzYiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiIqRi9GLylJImhHRiVGMUYzRi8qKCNGLyIjP0YvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiJCsiRi9GN0YvRjNGL0YyRi9GLw==">LCgqJiwoJkkieUc2IjYjIiM2IiIiKiYiIiNGKiZGJjYjIiM1RiohIiImRiY2IyIiKkYqRiopSSJoR0YnRixGMEYqKigjRioiIz9GKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiQrIkYqRjRGKkYwRipGLUYqRio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzYsKComLCgmSSJ5R0YlNiMiIzciIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiM1Ri9GLylJImhHRiVGMUYzRi8qKCNGLyIjQUYvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiJEAiRi9GN0YvRjNGL0YyRi9GLw==">LCgqJiwoJkkieUc2IjYjIiM3IiIiKiYiIiNGKiZGJjYjIiM2RiohIiImRiY2IyIjNUYqRiopSSJoR0YnRixGMEYqKigjRioiI0FGKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiRAIkYqRjRGKkYwRipGLUYqRio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzcsKComLCgmSSJ5R0YlNiMiIzgiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiM2Ri9GLylJImhHRiVGMUYzRi8qKCNGLyIjQ0YvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiJFciRi9GN0YvRjNGL0YyRi9GLw==">LCgqJiwoJkkieUc2IjYjIiM4IiIiKiYiIiNGKiZGJjYjIiM3RiohIiImRiY2IyIjNkYqRiopSSJoR0YnRixGMEYqKigjRioiI0NGKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiRXIkYqRjRGKkYwRipGLUYqRio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzgsKComLCgmSSJ5R0YlNiMiIzkiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiM3Ri9GLylJImhHRiVGMUYzRi8qKCNGLyIjRUYvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiJHAiRi9GN0YvRjNGL0YyRi9GLw==">LCgqJiwoJkkieUc2IjYjIiM5IiIiKiYiIiNGKiZGJjYjIiM4RiohIiImRiY2IyIjN0YqRiopSSJoR0YnRixGMEYqKigjRioiI0VGKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiRwIkYqRjRGKkYwRipGLUYqRio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzksKComLCgmSSJ5R0YlNiMiIzoiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiM4Ri9GLylJImhHRiVGMUYzRi8qKCNGLyIjR0YvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiJCc+Ri9GN0YvRjNGL0YyRi9GLw==">LCgqJiwoJkkieUc2IjYjIiM6IiIiKiYiIiNGKiZGJjYjIiM5RiohIiImRiY2IyIjOEYqRiopSSJoR0YnRixGMEYqKigjRioiI0dGKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiQnPkYqRjRGKkYwRipGLUYqRio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzosKComLCgmSSJ5R0YlNiMiIzsiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiM5Ri9GLylJImhHRiVGMUYzRi8qKCNGLyIjSUYvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiJEQjRi9GN0YvRjNGL0YyRi9GLw==">LCgqJiwoJkkieUc2IjYjIiM7IiIiKiYiIiNGKiZGJjYjIiM6RiohIiImRiY2IyIjOUYqRiopSSJoR0YnRixGMEYqKigjRioiI0lGKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiREI0YqRjRGKkYwRipGLUYqRio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzssKComLCgmSSJ5R0YlNiMiIzwiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiM6Ri9GLylJImhHRiVGMUYzRi8qKCNGLyIjS0YvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiJGMjRi9GN0YvRjNGL0YyRi9GLw==">LCgqJiwoJkkieUc2IjYjIiM8IiIiKiYiIiNGKiZGJjYjIiM7RiohIiImRiY2IyIjOkYqRiopSSJoR0YnRixGMEYqKigjRioiI0tGKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiRjI0YqRjRGKkYwRipGLUYqRio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzwsKComLCgmSSJ5R0YlNiMiIz0iIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiM7Ri9GLylJImhHRiVGMUYzRi8qKCNGLyIjTUYvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiJCpHRi9GN0YvRjNGL0YyRi9GLw==">LCgqJiwoJkkieUc2IjYjIiM9IiIiKiYiIiNGKiZGJjYjIiM8RiohIiImRiY2IyIjO0YqRiopSSJoR0YnRixGMEYqKigjRioiI01GKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiQqR0YqRjRGKkYwRipGLUYqRio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIz0sKComLCgmSSJ5R0YlNiMiIz4iIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiM8Ri9GLylJImhHRiVGMUYzRi8qKCNGLyIjT0YvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiJEMkRi9GN0YvRjNGL0YyRi9GLw==">LCgqJiwoJkkieUc2IjYjIiM+IiIiKiYiIiNGKiZGJjYjIiM9RiohIiImRiY2IyIjPEYqRiopSSJoR0YnRixGMEYqKigjRioiI09GKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiRDJEYqRjRGKkYwRipGLUYqRio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIz4sKComLCgmSSJ5R0YlNiMiIz8iIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiM9Ri9GLylJImhHRiVGMUYzRi8qKCNGLyIjUUYvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiJGgkRi9GN0YvRjNGL0YyRi9GLw==">LCgqJiwoJkkieUc2IjYjIiM/IiIiKiYiIiNGKiZGJjYjIiM+RiohIiImRiY2IyIjPUYqRiopSSJoR0YnRixGMEYqKigjRioiI1FGKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiRoJEYqRjRGKkYwRipGLUYqRio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIz8sKComLCgmSSJ5R0YlNiMiI0AiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiM+Ri9GLylJImhHRiVGMUYzRi8qKCNGLyIjU0YvRjdGMywmRitGL0Y0RjNGL0YvKigpSSdsYW1iZGFHRiVGMUYvLCZGL0YvKiYiJCslRi9GN0YvRjNGL0YyRi9GLw==">LCgqJiwoJkkieUc2IjYjIiNAIiIiKiYiIiNGKiZGJjYjIiM/RiohIiImRiY2IyIjPkYqRiopSSJoR0YnRixGMEYqKigjRioiI1NGKkY0RjAsJkYlRipGMUYwRipGKiooKUknbGFtYmRhR0YnRixGKiwmRipGKiomIiQrJUYqRjRGKkYwRipGLUYqRio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The additional equation for the eigenvalue is:</Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eqeig:=subs(diff(y(x),x)=dydxf,y(x)=y[0],bc3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmRXFlaWdHNiIsJiZJInlHRiQ2IyIiISIiIkYqISIi">LCYmSSJ5RzYiNiMiIiEiIiJGKCEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">h:=L/(N+1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiaEc2IiMiIiIiI0A=">IyIiIiIjQA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The finite difference equations are stored in eqs:</Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=seq(eval(subs(Phi=1,Eq[i])),i=0..N+1),Eqeig;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The dependent variables are stored in vars:</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=seq(y[i],i=0..N+1),lambda;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkldmFyc0c2IjY5JkkieUdGJDYjIiIhJkYnNiMiIiImRic2IyIiIyZGJzYjIiIkJkYnNiMiIiUmRic2IyIiJiZGJzYjIiInJkYnNiMiIigmRic2IyIiKSZGJzYjIiIqJkYnNiMiIzUmRic2IyIjNiZGJzYjIiM3JkYnNiMiIzgmRic2IyIjOSZGJzYjIiM6JkYnNiMiIzsmRic2IyIjPCZGJzYjIiM9JkYnNiMiIz4mRic2IyIjPyZGJzYjIiNASSdsYW1iZGFHRiQ=">NjkmSSJ5RzYiNiMiIiEmRiQ2IyIiIiZGJDYjIiIjJkYkNiMiIiQmRiQ2IyIiJSZGJDYjIiImJkYkNiMiIicmRiQ2IyIiKCZGJDYjIiIpJkYkNiMiIiomRiQ2IyIjNSZGJDYjIiM2JkYkNiMiIzcmRiQ2IyIjOCZGJDYjIiM5JkYkNiMiIzomRiQ2IyIjOyZGJDYjIiM8JkYkNiMiIz0mRiQ2IyIjPiZGJDYjIiM/JkYkNiMiI0BJJ2xhbWJkYUdGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">These variables are solved as:</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">fsolve({eqs},{vars});</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">PDkvJkkieUc2IjYjIiNAJCIiIUYqLyZGJTYjRiokIisrKysrNSEiKi9JJ2xhbWJkYUdGJiQhK3JVJHBsJ0YwLyZGJTYjIiM2JCErQ044d1AhIzUvJkYlNiMiIzckISttc1M4VUY7LyZGJTYjIiM4JCErYEYnPk0lRjsvJkYlNiMiIzkkIStEWiY9PyVGOy8mRiU2IyIjOiQhKzFbI1wlUUY7LyZGJTYjIiM7JCErS3IpeUskRjsvJkYlNiMiIiMkIitPUCM+LSpGOy8mRiU2IyIiJCQiK24pKTRqeUY7LyZGJTYjIiImJCIrJSlHaWpZRjsvJkYlNiMiIiUkIisyaSM+UCdGOy8mRiU2IyIiJyQiK2Y1L2tHRjsvJkYlNiMiIigkIiskKlJNKDQiRjsvJkYlNiMiIiIkIitNNFtiKCpGOy8mRiU2IyIjPiQhK29jaE44RjsvJkYlNiMiIz8kIStwT29UbCEjNi8mRiU2IyIiKSQhK211dl9fRmpxLyZGJTYjIiIqJCErTyxgOT5GOy8mRiU2IyIjNSQhK2BPdzNJRjsvJkYlNiMiIzwkISsoKjQ6MUZGOy8mRiU2IyIjPSQhKyMzJCopRz9GOw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Since there are multiple solutions, one has to provide the range for the dependent variables.  The dependent variable y varies between 0 and 1 and the eigenvalue is solved in the range of 0.4.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=seq(y[i]=-1..1,i=0..N+1),lambda=0..4;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkldmFyc0c2IjY5LyZJInlHRiQ2IyIiITshIiIiIiIvJkYoNiNGLUYrLyZGKDYjIiIjRisvJkYoNiMiIiRGKy8mRig2IyIiJUYrLyZGKDYjIiImRisvJkYoNiMiIidGKy8mRig2IyIiKEYrLyZGKDYjIiIpRisvJkYoNiMiIipGKy8mRig2IyIjNUYrLyZGKDYjIiM2RisvJkYoNiMiIzdGKy8mRig2IyIjOEYrLyZGKDYjIiM5RisvJkYoNiMiIzpGKy8mRig2IyIjO0YrLyZGKDYjIiM8RisvJkYoNiMiIz1GKy8mRig2IyIjPkYrLyZGKDYjIiM/RisvJkYoNiMiI0BGKy9JJ2xhbWJkYUdGJDtGKkY8">NjkvJkkieUc2IjYjIiIhOyEiIiIiIi8mRiU2I0YrRikvJkYlNiMiIiNGKS8mRiU2IyIiJEYpLyZGJTYjIiIlRikvJkYlNiMiIiZGKS8mRiU2IyIiJ0YpLyZGJTYjIiIoRikvJkYlNiMiIilGKS8mRiU2IyIiKkYpLyZGJTYjIiM1RikvJkYlNiMiIzZGKS8mRiU2IyIjN0YpLyZGJTYjIiM4RikvJkYlNiMiIzlGKS8mRiU2IyIjOkYpLyZGJTYjIiM7RikvJkYlNiMiIzxGKS8mRiU2IyIjPUYpLyZGJTYjIiM+RikvJkYlNiMiIz9GKS8mRiU2IyIjQEYpL0knbGFtYmRhR0YmO0YoRjo=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L54" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution obtained in stored in sol[1] and plotted:</Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol[1]:=fsolve({eqs},{vars});</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">assign(sol[1]):</Text-field>
</Input>
</Group>
<Group labelreference="L55" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The first eigenvalue is given by:</Text-field>
</Input>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">l[1]:=lambda;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJImxHNiI2IyIiIiQiK0EpPkJxIyEiKg==">JCIrQSk+QnEjISIq</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The first eigenfunction is plotted here:</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([seq([i*h,y[i]],i=0..N+1)],thickness=4,axes=boxed,labels=[x,y]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">NigtJSdDVVJWRVNHNiQ3ODckJCIiISEiIiQiIzUhIiI3JCQiMjt3Lz53Lz53JSEjPSQiKyU+bSllKiohIzU3JCQiMUImNFFfNFFfKiEjPCQiK3ZaWU4pKiEjNTckJCIyJkc5ZEc5ZEc5ISM8JCIrM0pKSycqISM1NyQkIjJaIT53Lz53Lz4hIzwkIiskNHpLTiohIzU3JCQiMjNRXzRRXzRRIyEjPCQiKk12TisqISIqNyQkIjFkRzlkRzlkRyEjOyQiKyN5KycqZSkhIzU3JCQiMUxMTExMTExMISM7JCIrWCNRKD0iKSEjNTckJCIyJDRRXzRRXzRRISM8JCIrc0s3KmYoISM1NyQkIjJiRzlkRzlkRyUhIzwkIisieiVSUnEhIzU3JCQiMjt3Lz53Lz53JSEjPCQiK0p4VltrISM1NyQkIjFRXzRRXzRRXyEjOyQiKyVIRl4kZSEjNTckJCIxOWRHOWRHOWQhIzskIisoKVEzM18hIzU3JCQiMSI+dy8+dy8+JyEjOyQiK0JtV3ZYISM1NyQkIjFtbW1tbW1tbSEjOyQiKzo9bldSISM1NyQkIjFWciZHOWRHOSghIzskIisuN09BTCEjNTckJCIxPncvPncvPnchIzskIitKRjc5RiEjNTckJCIxJjRRXzRRXzQpISM7JCIrI3lrVzcjISM1NyQkIjFyJkc5ZEc5ZCkhIzskIiskekFuYiIhIzU3JCQiMVshPncvPncvKiEjOyQiKyVROkksIiEjNTckJCIxQiY0UV80UV8qISM7JCIrLlZEVVwhIzY3JCQiIzUhIiIkIiIhISIiLSUmQ09MT1JHNiYlJFJHQkckIiM1ISIiJCIiISEiIiQiIiEhIiItJStBWEVTTEFCRUxTRzYnLUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2NVEieDYiLyUnZmFtaWx5R1EhNiIvJSVzaXplR1EjMTA2Ii8lJWJvbGRHUSZmYWxzZTYiLyUnaXRhbGljR1EldHJ1ZTYiLyUqdW5kZXJsaW5lR1EmZmFsc2U2Ii8lKnN1YnNjcmlwdEdRJmZhbHNlNiIvJSxzdXBlcnNjcmlwdEdRJmZhbHNlNiIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXTYiLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV02Ii8lJ29wYXF1ZUdRJmZhbHNlNiIvJStleGVjdXRhYmxlR1EmZmFsc2U2Ii8lKXJlYWRvbmx5R1EmZmFsc2U2Ii8lKWNvbXBvc2VkR1EmZmFsc2U2Ii8lKmNvbnZlcnRlZEdRJmZhbHNlNiIvJStpbXNlbGVjdGVkR1EmZmFsc2U2Ii8lLHBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJmZhbHNlNiIvJSxtYXRodmFyaWFudEdRJ2l0YWxpYzYiLUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2NVEieTYiLyUnZmFtaWx5R1EhNiIvJSVzaXplR1EjMTA2Ii8lJWJvbGRHUSZmYWxzZTYiLyUnaXRhbGljR1EldHJ1ZTYiLyUqdW5kZXJsaW5lR1EmZmFsc2U2Ii8lKnN1YnNjcmlwdEdRJmZhbHNlNiIvJSxzdXBlcnNjcmlwdEdRJmZhbHNlNiIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXTYiLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV02Ii8lJ29wYXF1ZUdRJmZhbHNlNiIvJStleGVjdXRhYmxlR1EmZmFsc2U2Ii8lKXJlYWRvbmx5R1EmZmFsc2U2Ii8lKWNvbXBvc2VkR1EmZmFsc2U2Ii8lKmNvbnZlcnRlZEdRJmZhbHNlNiIvJStpbXNlbGVjdGVkR1EmZmFsc2U2Ii8lLHBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJmZhbHNlNiIvJSxtYXRodmFyaWFudEdRJ2l0YWxpYzYiLSUlRk9OVEc2JSUhRyUhRyIjNSUrSE9SSVpPTlRBTEclK0hPUklaT05UQUxHLSUqVEhJQ0tORVNTRzYjIiIlLSUqQVhFU1NUWUxFRzYjJSRCT1hHLSUoU0NBTElOR0c2IyUuVU5DT05TVFJBSU5FREctJSVST09URzYnLSUpQk9VTkRTX1hHNiMkIiQhXCEiIi0lKUJPVU5EU19ZRzYjJCIkPyIhIiItJS1CT1VORFNfV0lEVEhHNiMkIiUhUSQhIiItJS5CT1VORFNfSEVJR0hURzYjJCIlU0MhIiItJSlDSElMRFJFTkc2Ig==</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[1]:=plot([seq([i*h,y[i]],i=0..N+1)],thickness=4,axes=boxed,labels=[x,y]):</Text-field>
</Input>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 do unassign('y[i]'):od:</Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">unassign('lambda'):</Text-field>
</Input>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">M:=4;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTUc2IiIiJQ==">IiIl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The next three eigenvalues are found by changing the range in increments of 4:</Text-field>
</Input>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for j from 2 to M do </Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=seq(y[i]=-1..1,i=0..N+1),lambda=l[j-1]+1..l[j-1]+4;</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol[j]:=fsolve({eqs},{vars});</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">assign(sol[j]):</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">l[j]:=lambda;</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[j]:=plot([seq([i*h,y[i]],i=0..N+1)],thickness=4,axes=boxed,labels=[x,y]):</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 do unassign('y[i]'):od:</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">unassign('lambda'):</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">od:</Text-field>
</Input>
</Group>
<Group labelreference="L58" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The same program was run rerun for N=20 node points.  The results obtained are:</Text-field>
</Input>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(seq(l[i],i=1..M));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiYkIitBKT5CcSMhIiokIityVSRwbCdGJSQiK11BKSllNSEiKSQiK1tneVg5Rio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L59" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Even after using N=30 interior node points we get only two digit accuracy with the exact solution.  In addition, we observe more errors for  higher eigenvalues than for the lower eigenvalues.</Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({seq(p[i],i=1..M)});</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">[encoded data, 5180 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>