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<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="Normal257" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="4" linespacing="0.0" spaceabove="0" spacebelow="0" 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=""/>
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<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="L76" drawlabel="true">
<Input>
<Text-field style="Heading 3" layout="Heading 3"><Font italic="false">Example 5.8</Font></Text-field>
</Input>
</Group>
<Group labelreference="L77" 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(linalg):with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ge1:=diff(u1(x,t),t)=diff(u1(x,t),x$2)-Phi^2*u1(x,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZ2UxRzYiLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSN1MUdGJDYkSSJ4R0YkSSJ0R0YkRi4sJi1GJzYkRiotSSIkR0YoNiRGLSIiIyIiIiomKUkkUGhpR0YkRjVGNkYqRjYhIiI=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSN1MUc2IjYkSSJ4R0YpSSJ0R0YpRiwsJi1GJDYkLUYkNiRGJ0YrRisiIiIqJilJJFBoaUdGKSIiI0YyRidGMiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ge2:=diff(u2(x,t),t)=diff(u2(x,t),x$2)-Phi^2*u2(x,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZ2UyRzYiLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSN1MkdGJDYkSSJ4R0YkSSJ0R0YkRi4sJi1GJzYkRiotSSIkR0YoNiRGLSIiIyIiIiomKUkkUGhpR0YkRjVGNkYqRjYhIiI=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSN1Mkc2IjYkSSJ4R0YpSSJ0R0YpRiwsJi1GJDYkLUYkNiRGJ0YrRisiIiIqJilJJFBoaUdGKSIiI0YyRidGMiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=u1(x,t)-1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLCYtSSN1MUdGJDYkSSJ4R0YkSSJ0R0YkIiIiRishIiI=">LCYtSSN1MUc2IjYkSSJ4R0YlSSJ0R0YlIiIiRikhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bcalpha:=diff(u1(x,t),x)=diff(u2(x,t),x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkoYmNhbHBoYUc2Ii8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkjdTFHRiQ2JEkieEdGJEkidEdGJEYtLUYnNiQtSSN1MkdGJEYsRi0=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSN1MUc2IjYkSSJ4R0YpSSJ0R0YpRistRiQ2JC1JI3UyR0YpRipGKw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=diff(u2(x,t),x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLUklZGlmZkclKnByb3RlY3RlZEc2JC1JI3UyR0YkNiRJInhHRiRJInRHRiRGLA==">LUklZGlmZkclKnByb3RlY3RlZEc2JC1JI3UyRzYiNiRJInhHRihJInRHRihGKg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IC1:=u1(x,0)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkSUMxRzYiLy1JI3UxR0YkNiRJInhHRiQiIiFGKg==">Ly1JI3UxRzYiNiRJInhHRiUiIiFGKA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IC2:=u2(x,0)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkSUMyRzYiLy1JI3UyR0YkNiRJInhHRiQiIiFGKg==">Ly1JI3UyRzYiNiRJInhHRiUiIiFGKA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> The boundary condition u1(alpha,t) = u2(alpha,t) is satisfied by default.</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> Let N and M be the number of node points in region 1 and region 2 respectively.</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=5;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTkc2IiIiJg==">IiIm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">M:=5;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTUc2IiIiJg==">IiIm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">alpha:=0.25;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmYWxwaGFHNiIkIiNEISIj">JCIjRCEiIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Phi:=5;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkUGhpRzYiIiIm">IiIm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxf:=1/2*(-u[2](t)-3*u[0](t)+4*u[1](t))/h1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGZHNiIsJCooIyIiIiIiI0YoLCgtJkkidUdGJDYjRik2I0kidEdGJCEiIiomIiIkRigtJkYtNiMiIiFGL0YoRjEqJiIiJUYoLSZGLTYjRihGL0YoRihGKEkjaDFHRiRGMUYo">LCQqKCMiIiIiIiNGJSwoLSZJInVHNiI2I0YmNiNJInRHRishIiIqJiIiJEYlLSZGKjYjIiIhRi1GJUYvKiYiIiVGJS0mRio2I0YlRi1GJUYlRiVJI2gxR0YrRi9GJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxb:=1/2*(u[N+M](t)+3*u[N+M+2](t)-4*u[N+M+1](t))/h2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGJHNiIsJCooIyIiIiIiI0YoLCgtJkkidUdGJDYjIiM1NiNJInRHRiRGKComIiIkRigtJkYtNiMiIzdGMEYoRigqJiIiJUYoLSZGLTYjIiM2RjBGKCEiIkYoSSNoMkdGJEY+Rig=">LCQqKCMiIiIiIiNGJSwoLSZJInVHNiI2IyIjNTYjSSJ0R0YrRiUqJiIiJEYlLSZGKjYjIiM3Ri5GJUYlKiYiIiVGJS0mRio2IyIjNkYuRiUhIiJGJUkjaDJHRitGPEYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxb2:=1/2*(u[N-1](t)+3*u[N+1](t)-4*u[N](t))/h1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknZHlkeGIyRzYiLCQqKCMiIiIiIiNGKCwoLSZJInVHRiQ2IyIiJTYjSSJ0R0YkRigqJiIiJEYoLSZGLTYjIiInRjBGKEYoKiZGL0YoLSZGLTYjIiImRjBGKCEiIkYoSSNoMUdGJEY9Rig=">LCQqKCMiIiIiIiNGJSwoLSZJInVHNiI2IyIiJTYjSSJ0R0YrRiUqJiIiJEYlLSZGKjYjIiInRi5GJUYlKiZGLUYlLSZGKjYjIiImRi5GJSEiIkYlSSNoMUdGK0Y7RiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxf2:=1/2*(-u[N+3](t)-3*u[N+1](t)+4*u[N+2](t))/h2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknZHlkeGYyRzYiLCQqKCMiIiIiIiNGKCwoLSZJInVHRiQ2IyIiKTYjSSJ0R0YkISIiKiYiIiRGKC0mRi02IyIiJ0YwRihGMiomIiIlRigtJkYtNiMiIihGMEYoRihGKEkjaDJHRiRGMkYo">LCQqKCMiIiIiIiNGJSwoLSZJInVHNiI2IyIiKTYjSSJ0R0YrISIiKiYiIiRGJS0mRio2IyIiJ0YuRiVGMComIiIlRiUtJkYqNiMiIihGLkYlRiVGJUkjaDJHRitGMEYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> The first and second derivatives are in the governing equation are converted to finite difference form as:</Text-field>
</Input>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydx:=piecewise(i&lt;N+1,1/2/h1*(u[m+1](t)-u[m-1](t)),i&gt;N+1,1/2/h2*(u[m+1](t)-u[m-1](t)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklZHlkeEc2Ii1JKlBJRUNFV0lTRUdGJDYkNyQsJCooIyIiIiIiI0YsSSNoMUdGJCEiIiwmLSZJInVHRiQ2IywmSSJtR0YkRixGLEYsNiNJInRHRiRGLC0mRjM2IywmRjZGLEYsRi9GN0YvRixGLDJJImlHRiQiIic3JCwkKihGK0YsSSNoMkdGJEYvRjBGLEYsMkY/Rj4=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkqbXZlcmJhdGltR0YkNiNRKCUlZHlkeEdGJy1JI21vR0YkNi1RIzo9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1E4LSUqUElFQ0VXSVNFRzYkJSI/RyUiP0dGJw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">d2ydx2:=piecewise(i&lt;N+1,1/h1^2*(u[m-1](t)-2*u[m](t)+u[m+1](t)),i&gt;N+1,1/h2^2*(u[m-1](t)-2*u[m](t)+u[m+1](t)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknZDJ5ZHgyRzYiLUkqUElFQ0VXSVNFR0YkNiQ3JComKUkjaDFHRiQiIiMhIiIsKC0mSSJ1R0YkNiMsJkkibUdGJCIiIkY1Ri02I0kidEdGJEY1KiZGLEY1LSZGMTYjRjRGNkY1Ri0tJkYxNiMsJkY0RjVGNUY1RjZGNUY1MkkiaUdGJCIiJzckKiYpSSNoMkdGJEYsRi1GLkY1MkZCRkE=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkqbXZlcmJhdGltR0YkNiNRKiUnZDJ5ZHgyR0YnLUkjbW9HRiQ2LVEjOj1GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1GLDYjUTgtJSpQSUVDRVdJU0VHNiQlIj9HJSI/R0Yn</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=subs(diff(u1(x,t),x)=dydxf,u1(x,t)=u[0](t),x=0,bc1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLCYtJkkidUdGJDYjIiIhNiNJInRHRiQiIiJGLSEiIg==">LCYtJkkidUc2IjYjIiIhNiNJInRHRiYiIiJGKyEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=subs(diff(u2(x,t),x)=dydxb,u2(x,t)=u[N+M+2](t),bc2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLCQqKCMiIiIiIiNGKCwoLSZJInVHRiQ2IyIjNTYjSSJ0R0YkRigqJiIiJEYoLSZGLTYjIiM3RjBGKEYoKiYiIiVGKC0mRi02IyIjNkYwRighIiJGKEkjaDJHRiRGPkYo">LCQqKCMiIiIiIiNGJSwoLSZJInVHNiI2IyIjNTYjSSJ0R0YrRiUqJiIiJEYlLSZGKjYjIiM3Ri5GJUYlKiYiIiVGJS0mRio2IyIjNkYuRiUhIiJGJUkjaDJHRitGPEYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bcalpha:=subs(diff(u1(x,t),x)=dydxb2,diff(u2(x,t),x)=dydxf2,u1(x,t)=u[N+1](t),u2(x,t)=u[N+1](t),bcalpha);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkoYmNhbHBoYUc2Ii8sJCooIyIiIiIiI0YpLCgtJkkidUdGJDYjIiIlNiNJInRHRiRGKSomIiIkRiktJkYuNiMiIidGMUYpRikqJkYwRiktJkYuNiMiIiZGMUYpISIiRilJI2gxR0YkRj5GKSwkKihGKEYpLCgtJkYuNiMiIilGMUY+RjNGPiomRjBGKS0mRi42IyIiKEYxRilGKUYpSSNoMkdGJEY+Rik=">LywkKigjIiIiIiIjRiYsKC0mSSJ1RzYiNiMiIiU2I0kidEdGLEYmKiYiIiRGJi0mRis2IyIiJ0YvRiZGJiomRi5GJi0mRis2IyIiJkYvRiYhIiJGJkkjaDFHRixGPEYmLCQqKEYlRiYsKC0mRis2IyIiKUYvRjxGMUY8KiZGLkYmLSZGKzYjIiIoRi9GJkYmRiZJI2gyR0YsRjxGJg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[0]:=bc1; </Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiEsJi0mSSJ1R0YlRiY2I0kidEdGJSIiIkYuISIi">LCYtJkkidUc2IjYjIiIhNiNJInRHRiYiIiJGKyEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[N+1]:=bcalpha; </Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIicvLCQqKCMiIiIiIiNGLCwoLSZJInVHRiU2IyIiJTYjSSJ0R0YlRiwqJiIiJEYsLSZGMUYmRjRGLEYsKiZGM0YsLSZGMTYjIiImRjRGLCEiIkYsSSNoMUdGJUY/RiwsJCooRitGLCwoLSZGMTYjIiIpRjRGP0Y2Rj8qJkYzRiwtJkYxNiMiIihGNEYsRixGLEkjaDJHRiVGP0Ys">LywkKigjIiIiIiIjRiYsKC0mSSJ1RzYiNiMiIiU2I0kidEdGLEYmKiYiIiRGJi0mRis2IyIiJ0YvRiZGJiomRi5GJi0mRis2IyIiJkYvRiYhIiJGJkkjaDFHRixGPEYmLCQqKEYlRiYsKC0mRis2IyIiKUYvRjxGMUY8KiZGLkYmLSZGKzYjIiIoRi9GJkYmRiZJI2gyR0YsRjxGJg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[N+M+2]:=bc2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzcsJCooIyIiIiIiI0YrLCgtJkkidUdGJTYjIiM1NiNJInRHRiVGKyomIiIkRistJkYwRiZGM0YrRisqJiIiJUYrLSZGMDYjIiM2RjNGKyEiIkYrSSNoMkdGJUY/Ris=">LCQqKCMiIiIiIiNGJSwoLSZJInVHNiI2IyIjNTYjSSJ0R0YrRiUqJiIiJEYlLSZGKjYjIiM3Ri5GJUYlKiYiIiVGJS0mRio2IyIjNkYuRiUhIiJGJUkjaDJHRitGPEYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> When the governing equation is converted to finite difference form x has to be defined according to region 1 and region 2.  The finite difference equations for region 1 are:</Text-field>
</Input>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N do eq[i]:=diff(u[i](t),t)= subs(diff(u1(x,t),x$2) = subs(m=i,d2ydx2),diff(u1(x,t),x) = subs(m=i,dydx),u1(x,t)=u[i](t),x=i*h1,rhs(ge1));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJI2gxR0YlIiIjISIiLCgtJkYvNiMiIiFGMEYnKiZGNkYnRi1GJ0Y3LSZGLzYjRjZGMEYnRidGJyomIiNERidGLUYnRjc=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIiNiNJInRHRipGLiwmKiYpSSNoMUdGKiIiIyEiIiwoLSZGKTYjIiIhRi1GLComRjNGLEYnRixGNC0mRik2I0YzRi1GLEYsRiwqJiIjREYsRidGLEY0</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJI2gxR0YlRichIiIsKC0mRi82IyIiIkYwRjsqJkYnRjtGLUY7RjYtJkYvNiMiIiRGMEY7RjtGOyomIiNERjtGLUY7RjY=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIjNiNJInRHRipGLiwmKiYpSSNoMUdGKkYsISIiLCgtJkYpNiMiIiJGLUY4KiZGLEY4RidGOEYzLSZGKTYjIiIkRi1GOEY4RjgqJiIjREY4RidGOEYz</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJI2gxR0YlIiIjISIiLCgtJkYvNiNGNkYwIiIiKiZGNkY8Ri1GPEY3LSZGLzYjIiIlRjBGPEY8RjwqJiIjREY8Ri1GPEY3">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIkNiNJInRHRipGLiwmKiYpSSNoMUdGKiIiIyEiIiwoLSZGKTYjRjNGLSIiIiomRjNGOUYnRjlGNC0mRik2IyIiJUYtRjlGOUY5KiYiI0RGOUYnRjlGNA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJI2gxR0YlIiIjISIiLCgtJkYvNiMiIiRGMCIiIiomRjZGPUYtRj1GNy0mRi82IyIiJkYwRj1GPUY9KiYiI0RGPUYtRj1GNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIlNiNJInRHRipGLiwmKiYpSSNoMUdGKiIiIyEiIiwoLSZGKTYjIiIkRi0iIiIqJkYzRjpGJ0Y6RjQtJkYpNiMiIiZGLUY6RjpGOiomIiNERjpGJ0Y6RjQ=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiYvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJI2gxR0YlIiIjISIiLCgtJkYvNiMiIiVGMCIiIiomRjZGPUYtRj1GNy0mRi82IyIiJ0YwRj1GPUY9KiYiI0RGPUYtRj1GNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiImNiNJInRHRipGLiwmKiYpSSNoMUdGKiIiIyEiIiwoLSZGKTYjIiIlRi0iIiIqJkYzRjpGJ0Y6RjQtJkYpNiMiIidGLUY6RjpGOiomIiNERjpGJ0Y6RjQ=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> eq[N+1] is given the boundary condition at the interface between region 1 and region 2. The finite difference equations for region 2 are:</Text-field>
</Input>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from N+2 to N+M+1 do eq[i]:=diff(u[i](t),t)= subs(diff(u2(x,t),x$2) = subs(m=i,d2ydx2),diff(u2(x,t),x) = subs(m=i,dydx),u2(x,t)=u[i](t),x=alpha+(i-N-1)*h2,rhs(ge2));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIigvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJI2gyR0YlIiIjISIiLCgtJkYvNiMiIidGMCIiIiomRjZGPUYtRj1GNy0mRi82IyIiKUYwRj1GPUY9KiYiI0RGPUYtRj1GNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIoNiNJInRHRipGLiwmKiYpSSNoMkdGKiIiIyEiIiwoLSZGKTYjIiInRi0iIiIqJkYzRjpGJ0Y6RjQtJkYpNiMiIilGLUY6RjpGOiomIiNERjpGJ0Y6RjQ=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIikvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJI2gyR0YlIiIjISIiLCgtJkYvNiMiIihGMCIiIiomRjZGPUYtRj1GNy0mRi82IyIiKkYwRj1GPUY9KiYiI0RGPUYtRj1GNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIpNiNJInRHRipGLiwmKiYpSSNoMkdGKiIiIyEiIiwoLSZGKTYjIiIoRi0iIiIqJkYzRjpGJ0Y6RjQtJkYpNiMiIipGLUY6RjpGOiomIiNERjpGJ0Y6RjQ=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiovLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJI2gyR0YlIiIjISIiLCgtJkYvNiMiIilGMCIiIiomRjZGPUYtRj1GNy0mRi82IyIjNUYwRj1GPUY9KiYiI0RGPUYtRj1GNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIqNiNJInRHRipGLiwmKiYpSSNoMkdGKiIiIyEiIiwoLSZGKTYjIiIpRi0iIiIqJkYzRjpGJ0Y6RjQtJkYpNiMiIzVGLUY6RjpGOiomIiNERjpGJ0Y6RjQ=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJI2gyR0YlIiIjISIiLCgtJkYvNiMiIipGMCIiIiomRjZGPUYtRj1GNy0mRi82IyIjNkYwRj1GPUY9KiYiI0RGPUYtRj1GNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiM1NiNJInRHRipGLiwmKiYpSSNoMkdGKiIiIyEiIiwoLSZGKTYjIiIqRi0iIiIqJkYzRjpGJ0Y6RjQtJkYpNiMiIzZGLUY6RjpGOiomIiNERjpGJ0Y6RjQ=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzYvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJI2gyR0YlIiIjISIiLCgtJkYvNiMiIzVGMCIiIiomRjZGPUYtRj1GNy0mRi82IyIjN0YwRj1GPUY9KiYiI0RGPUYtRj1GNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiM2NiNJInRHRipGLiwmKiYpSSNoMkdGKiIiIyEiIiwoLSZGKTYjIiM1Ri0iIiIqJkYzRjpGJ0Y6RjQtJkYpNiMiIzdGLUY6RjpGOiomIiNERjpGJ0Y6RjQ=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u[0](t):=(solve(eq[0],u[0](t)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiE2I0kidEdGJiIiIg==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u[N+1](t):=solve(eq[N+1],u[N+1](t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIic2I0kidEdGJiwkKigjIiIiIiIkRi4sKiomSSNoMkdGJkYuLSZGJTYjIiIlRilGLkYuKihGNkYuRjJGLi0mRiU2IyIiJkYpRi4hIiIqJkkjaDFHRiZGLi0mRiU2IyIiKUYpRi5GLiooRjZGLkY+Ri4tJkYlNiMiIihGKUYuRjxGLiwmRjJGLkY+Ri5GPEY8">LCQqKCMiIiIiIiRGJSwqKiZJI2gyRzYiRiUtJkkidUdGKjYjIiIlNiNJInRHRipGJUYlKihGL0YlRilGJS0mRi02IyIiJkYwRiUhIiIqJkkjaDFHRipGJS0mRi02IyIiKUYwRiVGJSooRi9GJUY5RiUtJkYtNiMiIihGMEYlRjdGJSwmRilGJUY5RiVGN0Y3</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u[N+M+2](t):=solve(eq[N+M+2],u[N+M+2](t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIzc2I0kidEdGJiwmKiYjIiIiIiIkRi4tJkYlNiMiIzVGKUYuISIiKiYjIiIlRi9GLi0mRiU2IyIjNkYpRi5GLg==">LCYqJiMiIiIiIiRGJS0mSSJ1RzYiNiMiIzU2I0kidEdGKkYlISIiKiYjIiIlRiZGJS0mRik2IyIjNkYtRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N do eq[i]:=eval(eq[i]):od:for i from N+2 to N+M+1 do eq[i]:=eval(eq[i]);od:</Text-field>
</Input>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=[seq(rhs(eq[j]),j=1..N),seq(rhs(eq[N+1+j]),j=1..M)]:</Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=[seq(u[i](t),i=1..N),seq(u[N+1+i](t),i=1..M)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiWUc2IjcsLSZJInVHRiQ2IyIiIjYjSSJ0R0YkLSZGKDYjIiIjRistJkYoNiMiIiRGKy0mRig2IyIiJUYrLSZGKDYjIiImRistJkYoNiMiIihGKy0mRig2IyIiKUYrLSZGKDYjIiIqRistJkYoNiMiIzVGKy0mRig2IyIjNkYr">NywtJkkidUc2IjYjIiIiNiNJInRHRiYtJkYlNiMiIiNGKS0mRiU2IyIiJEYpLSZGJTYjIiIlRiktJkYlNiMiIiZGKS0mRiU2IyIiKEYpLSZGJTYjIiIpRiktJkYlNiMiIipGKS0mRiU2IyIjNUYpLSZGJTYjIiM2Rik=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=genmatrix(eqs,Y,'b1'):</Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b:=matrix(N+M,1):for i to N+M do b[i,1]:=-eval(b1[i]);od:evalm(b);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUknbWF0cml4RzYiNiM3LDcjKiQpSSNoMUdGJCIiIyEiIjcjIiIhRi1GLUYtRi1GLUYtRi1GLQ==">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">h1:=eval(alpha/(N+1));h2:=eval((1-alpha)/(M+1));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjaDFHNiIkIitubW1tVCEjNg==">JCIrbm1tbVQhIzY=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjaDJHNiIkIisrKytdNyEjNQ==">JCIrKysrXTchIzU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=map(eval,A):</Text-field>
</Input>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">if N+M &gt;4 then A:=map(evalf,A);end: </Text-field>
</Input>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=exponential(A,t):</Text-field>
</Input>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=map(evalf,mat):</Text-field>
</Input>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y0:=matrix(N+M,1):for i from 1 to N+M do Y0[i,1]:=0;od:evalm(Y0):</Text-field>
</Input>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">s1:=evalm(Y0+inverse(A)&amp;*b):</Text-field>
</Input>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=evalm(mat&amp;*s1-inverse(A)&amp;*b):</Text-field>
</Input>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=map(simplify,Y):</Text-field>
</Input>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N do u[i](t):=evalf((Y[i,1]));od:</Text-field>
</Input>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from N+2 to N+M+1 do u[i](t):=evalf((Y[i-1,1]));od:</Text-field>
</Input>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+M+2 do u[i](t):=eval(u[i](t));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiE2I0kidEdGJiIiIg==">IiIi</Equation></Text-field>
</Output>
<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>
<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>
<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>
<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>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiY2I0kidEdGJiw4KiYkIitLUjdDNiEjNiIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjLCQqJiQiK21pcU5AISInRjBGKkYwISIiRjBGPComJCIrIkctPDImRi9GMC1GMjYjLCQqJiQiK14/KXlpIkY7RjBGKkYwRjxGMEYwKiYkIisiPnReUSIhIzVGMC1GMjYjLCQqJiQiK0lLekMqKiEiKEYwRipGMEY8RjBGPComJCIraGAoSClHRklGMC1GMjYjLCQqJiQiK2xuN1FYRlBGMEYqRjBGPEYwRjAqJiQiK0Q3aiVcKiEjOEYwLUYyNiMsJComJCIrK0UoeWEjRlBGMEYqRjBGPEYwRjAqJiQiK1dlbk9JRi9GMC1GMjYjLCQqJiQiKyY0bVMnPkZQRjBGKkYwRjxGMEY8KiYkIitqJUcxYCJGSUYwLUYyNiMsJComJCIrL11tQjlGUEYwRipGMEY8RjBGPComJCIrTj1rRzxGSUYwLUYyNiMsJComJCIrOmElZiMqKSEiKUYwRipGMEY8RjBGPComJCIrI1EkKVJgIkZJRjAtRjI2IywkKiYkIittMyN6ciVGaXBGMEYqRjBGPEYwRjwqJiQiKzBkeWtPRi9GMC1GMjYjLCQqJiQiK1EkKVJYRkZpcEYwRipGMEY8RjBGPCQiKyUpSFQ+T0ZJRjA=">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</Equation></Text-field>
</Output>
<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>
<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>
<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>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIio2I0kidEdGJiw4KiYkIitWXWZjcSEjOyIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjLCQqJiQiK21pcU5AISInRjBGKkYwISIiRjBGMComJCIrPCJvcF4nISM6RjAtRjI2IywkKiYkIitePyl5aSJGO0YwRipGMEY8RjBGPComJCIrbzNqL3UhIzlGMC1GMjYjLCQqJiQiK0lLekMqKiEiKEYwRipGMEY8RjBGMComJCIrY2RBZEUhIzdGMC1GMjYjLCQqJiQiK2xuN1FYRlFGMEYqRjBGPEYwRjwqJiQiKyoqUTskRyQhIzZGMC1GMjYjLCQqJiQiKytFKHlhI0ZRRjBGKkYwRjxGMEYwKiYkIitDOypbJ0dGaW5GMC1GMjYjLCQqJiQiKyY0bVMnPkZRRjBGKkYwRjxGMEY8KiYkIis7bG0lPilGaW5GMC1GMjYjLCQqJiQiKy9dbUI5RlFGMEYqRjBGPEYwRjwqJiQiK1chSCYqZSIhIzVGMC1GMjYjLCQqJiQiKzphJWYjKikhIilGMEYqRjBGPEYwRjAqJiQiK3Epbz9EJEZpbkYwLUYyNiMsJComJCIrbTMjenIlRlxxRjBGKkYwRjxGMEY8KiYkIitQJVFGVCpGaW5GMC1GMjYjLCQqJiQiK1EkKVJYRkZccUYwRipGMEY8RjBGPCQiKz05ci9bRmluRjA=">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</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDgqJiQiKydbWnpHIyEjPCIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiQiK21pcU5AISInRidJInRHRi1GJyEiIkYnRjUqJiQiK28ocDgkRyEjO0YnLUYpNiMsJComJCIrXj8peWkiRjNGJ0Y0RidGNUYnRicqJiQiKz9wKlxtJiEjOkYnLUYpNiMsJComJCIrSUt6QyoqISIoRidGNEYnRjVGJ0Y1KiYkIitIKUcmKnkmISM4RictRik2IywkKiYkIitsbjdRWEZKRidGNEYnRjVGJ0YnKiYkIitJVCQpNEMhIzZGJy1GKTYjLCQqJiQiKytFKHlhI0ZKRidGNEYnRjVGJ0Y1KiYkIitccHhnIylGWEYnLUYpNiMsJComJCIrJjRtUyc+RkpGJ0Y0RidGNUYnRicqJiQiKzJ4UjY2ISM1RictRik2IywkKiYkIisvXW1COUZKRidGNEYnRjVGJ0Y1KiYkIitSWl9bYEZYRictRik2IywkKiYkIis6YSVmIyopISIpRidGNEYnRjVGJ0YnKiYkIit0XGN5dkZYRictRik2IywkKiYkIittMyN6ciVGZXBGJ0Y0RidGNUYnRicqJiQiK3VJN1g1RmVvRictRik2IywkKiYkIitRJClSWEZGZXBGJ0Y0RidGNUYnRjUkIitOMiMpSEZGWEYn</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIzY2I0kidEdGJiw4KiYkIit4KSl6KFslISM+IiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMsJComJCIrbWlxTkAhIidGMEYqRjAhIiJGMEYwKiYkIitgJj0qUXghIz1GMC1GMjYjLCQqJiQiK14/KXlpIkY7RjBGKkYwRjxGMEY8KiYkIitvK284RSEjO0YwLUYyNiMsJComJCIrSUt6QyoqISIoRjBGKkYwRjxGMEYwKiYkIiticzEoUichIzlGMC1GMjYjLCQqJiQiK2xuN1FYRlFGMEYqRjBGPEYwRjwqJiQiKydcR1tcJiEjN0YwLUYyNiMsJComJCIrK0UoeWEjRlFGMEYqRjBGPEYwRjAqJiQiK1dXd1BGISM2RjAtRjI2IywkKiYkIismNG1TJz5GUUYwRipGMEY8RjBGPComJCIrJipHLVtqRmNvRjAtRjI2IywkKiYkIisvXW1COUZRRjBGKkYwRjxGMEYwKiYkIitNSiZvMCIhIzVGMC1GMjYjLCQqJiQiKzphJWYjKikhIilGMEYqRjBGPEYwRjwqJiQiK2M3SHk6RmZwRjAtRjI2IywkKiYkIittMyN6ciVGXXFGMEYqRjBGPEYwRjAqJiQiKy08ISozNkZmcEYwLUYyNiMsJComJCIrUSQpUlhGRl1xRjBGKkYwRjxGMEY8JCIrd2lFQDxGY29GMA==">LDgqJiQiK3gpKXooWyUhIz4iIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkKiYkIittaXFOQCEiJ0YnSSJ0R0YtRichIiJGJ0YnKiYkIitgJj0qUXghIz1GJy1GKTYjLCQqJiQiK14/KXlpIkYzRidGNEYnRjVGJ0Y1KiYkIitvK284RSEjO0YnLUYpNiMsJComJCIrSUt6QyoqISIoRidGNEYnRjVGJ0YnKiYkIiticzEoUichIzlGJy1GKTYjLCQqJiQiK2xuN1FYRkpGJ0Y0RidGNUYnRjUqJiQiKydcR1tcJiEjN0YnLUYpNiMsJComJCIrK0UoeWEjRkpGJ0Y0RidGNUYnRicqJiQiK1dXd1BGISM2RictRik2IywkKiYkIismNG1TJz5GSkYnRjRGJ0Y1RidGNSomJCIrJipHLVtqRlxvRictRik2IywkKiYkIisvXW1COUZKRidGNEYnRjVGJ0YnKiYkIitNSiZvMCIhIzVGJy1GKTYjLCQqJiQiKzphJWYjKikhIilGJ0Y0RidGNUYnRjUqJiQiK2M3SHk6Rl9wRictRik2IywkKiYkIittMyN6ciVGZnBGJ0Y0RidGNUYnRicqJiQiKy08ISozNkZfcEYnLUYpNiMsJComJCIrUSQpUlhGRmZwRidGNEYnRjVGJ0Y1JCIrd2lFQDxGXG9GJw==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDgqJiQiKy9bJ1tBKSEjPSIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiQiK21pcU5AISInRidJInRHRi1GJyEiIkYnRicqJiQiKy5iKHAvIiEjO0YnLUYpNiMsJComJCIrXj8peWkiRjNGJ0Y0RidGNUYnRjUqJiQiKyQpSCNvQiMhIzpGJy1GKTYjLCQqJiQiK0lLekMqKiEiKEYnRjRGJ0Y1RidGJyomJCIrV195I3kjISM4RictRik2IywkKiYkIitsbjdRWEZKRidGNEYnRjVGJ0Y1KiYkIitWPSNmYCIhIzZGJy1GKTYjLCQqJiQiKytFKHlhI0ZKRidGNEYnRjVGJ0YnKiYkIiszXCVSUydGWEYnLUYpNiMsJComJCIrJjRtUyc+RkpGJ0Y0RidGNUYnRjUqJiQiK2Iqb29AIiEjNUYnLUYpNiMsJComJCIrL11tQjlGSkYnRjRGJ0Y1RidGJyomJCIrcTtVKGUiRmVvRictRik2IywkKiYkIis6YSVmIyopISIpRidGNEYnRjVGJ0Y1KiYkIis0JnA8Jj1GZW9GJy1GKTYjLCQqJiQiK20zI3pyJUZlcEYnRjRGJ0Y1RidGJyomJCIrWDc7STZGZW9GJy1GKTYjLCQqJiQiK1EkKVJYRkZlcEYnRjRGJ0Y1RidGNSQiK2M5MyZRIkZYRic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L82" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">setcolors([&quot;Red&quot;, &quot;Blue&quot;, &quot;LimeGreen&quot;, &quot;Goldenrod&quot;, &quot;maroon&quot;, &quot;DarkTurquoise&quot;, &quot;coral&quot;, &quot;aquamarine&quot;, &quot;magenta&quot;, &quot;khaki&quot;,  &quot;sienna&quot;, &quot;orange&quot;, &quot;yellow&quot;, &quot;gray&quot;]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyhRJFJlZDYiUSpMaW1lR3JlZW5GJFEqR29sZGVucm9kRiRRJUJsdWVGJFEtTWVkaXVtT3JjaGlkRiRRLkRhcmtUdXJxdW9pc2VGJA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L81" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pp:=plot([seq(u[i](t),i=0..N+M+2)],t=0..0.1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 20012 characters]">[encoded data, 19968 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L83" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pt:=textplot([[0.015,1.0,typeset(u[0],&quot;(t)&quot;),align=below],seq([0.02+i*0.005,evalf(subs(t=0.02+i*0.005,u[i](t))),typeset(u[i],&quot;(t)&quot;),align=above],i=1..N+M-2)]);</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="L55" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display([pp,pt],title=&quot;Figure 5.27.&quot;,thickness=3,axes=boxed,labels=[t,&quot;u&quot;]);</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, 56096 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tf:=0.1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdGZHNiIkIiIiISIi">JCIiIiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">MM:=30;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjTU1HNiIiI0k=">IiNJ</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L58" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T1:=[seq(tf*i/MM,i=0..MM)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVDFHNiI3QSQiIiFGJyQiK0xMTExMISM3JCIrbm1tbW1GKiQiKysrKys1ISM2JCIrTExMTDhGLyQiK25tbW07Ri8kIisrKysrP0YvJCIrTExMTEJGLyQiK25tbW1FRi8kIisrKysrSUYvJEYpRi8kIitubW1tT0YvJCIrKysrK1NGLyQiK0xMTExWRi8kIitubW1tWUYvJCIrKysrK11GLyQiK0xMTExgRi8kIitubW1tY0YvJCIrKysrK2dGLyQiK0xMTExqRi8kRixGLyQiKysrKytxRi8kIitMTExMdEYvJCIrbm1tbXdGLyQiKysrKyshKUYvJCIrTExMTCQpRi8kIitubW1tJylGLyQiKysrKyshKkYvJCIrTExMTCQqRi8kIitubW1tJypGLyRGLiEjNQ==">N0EkIiIhRiQkIitMTExMTCEjNyQiK25tbW1tRickIisrKysrNSEjNiQiK0xMTEw4RiwkIitubW1tO0YsJCIrKysrKz9GLCQiK0xMTExCRiwkIitubW1tRUYsJCIrKysrK0lGLCRGJkYsJCIrbm1tbU9GLCQiKysrKytTRiwkIitMTExMVkYsJCIrbm1tbVlGLCQiKysrKytdRiwkIitMTExMYEYsJCIrbm1tbWNGLCQiKysrKytnRiwkIitMTExMakYsJEYpRiwkIisrKysrcUYsJCIrTExMTHRGLCQiK25tbW13RiwkIisrKysrISlGLCQiK0xMTEwkKUYsJCIrbm1tbScpRiwkIisrKysrISpGLCQiK0xMTEwkKkYsJCIrbm1tbScqRiwkRishIzU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L59" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">PP:=matrix(N+M+3,MM+1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjUFBHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIzg7RioiI0o3Ig==">PTYiNiQ7IiIiIiM4O0YmIiNKRVxbbCE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L60" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N+M+3 do PP[i,1]:=0;od:</Text-field>
</Input>
</Group>
<Group labelreference="L61" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N+M+3 do for j from 2 to MM+1 do PP[i,j]:=evalf(subs(t=T1[j],u[i-1](t)));od;od:</Text-field>
</Input>
</Group>
<Group labelreference="L62" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalm(PP):</Text-field>
</Input>
</Group>
<Group labelreference="L63" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">i:='i';</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiaUc2IkYj">SSJpRzYi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L64" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">X:=piecewise(i&lt;N+3,(i-1)*h1,i&gt;N+2,alpha+(i-N-2)*h2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiWEc2Ii1JKlBJRUNFV0lTRUdGJDYkNyQsJiomJCIrbm1tbVQhIzYiIiJJImlHRiRGLkYuRishIiIyRi8iIik3JCwmJCIrKysrXWkhIzVGMComJCIrKysrXTdGN0YuRi9GLkYuMiIiKEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkqbXZlcmJhdGltR0YkNiNRJSUiWEdGJy1JI21vR0YkNi1RIzo9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1E4LSUqUElFQ0VXSVNFRzYkJSI/RyUiP0dGJw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L65" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(X,i=1..N+M+3,thickness=4,title=&quot;Figure Exp.5.28.&quot;,axes=boxed,labels=['i',&quot;X&quot;]);</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">[encoded data, 4164 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L66" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plotdata:=[seq([ seq([eval(X),T1[j],PP[i,j]], i=1..N+M+3)], j=1..MM+1)]:</Text-field>
</Input>
</Group>
<Group labelreference="L67" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">surfdata(plotdata,axes=boxed,title=&quot;Figure Exp. 5.29.&quot;,labels=[x,t,u],orientation=[-75,60]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" type="three-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0">[encoded data, 19148 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L68" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=diff(U(x),x$2)-Phi^2*U(x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIsJi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJVR0YkNiNJInhHRiQtSSIkR0YoNiRGLSIiIyIiIiomIiNERjJGKkYyISIi">LCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYkNiQtSSJVRzYiNiNJInhHRitGLUYtIiIiKiYiI0RGLkYpRi4hIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L69" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ua:=rhs(dsolve({eq,U(0)=1,D(U)(1)=0},U(x)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVWFHNiIsJiooLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMhIiYiIiIsJi1GKDYjIiImRi5GJ0YuISIiLUYoNiMsJComRjJGLkkieEdGJEYuRi5GLkYuKihGL0YzRjBGLi1GKDYjLCRGN0YzRi5GLg==">LCYqKC1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjISImIiIiLCYtRiU2IyIiJkYsRiRGLCEiIi1GJTYjLCQqJkYwRixJInhHRilGLEYsRixGLCooRi1GMUYuRiwtRiU2IywkRjVGMUYsRiw=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L70" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Flux:=-evalf(subs(x=0.,diff(Ua,x)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklRmx1eEc2IiQiK0JnYSoqXCEiKg==">JCIrQmdhKipcISIq</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L71" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">flux:=-dydxf;</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="L72" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">flux:=limit(flux,t=infinity);Flux;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklZmx1eEc2IiQiK1ciSGUqWyEiKg==">JCIrVyJIZSpbISIq</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIrQmdhKipcISIq</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L73" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Err:=abs(flux-Flux)/Flux*100;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkRXJyRzYiJCIrUGZfdT8hIio=">JCIrUGZfdT8hIio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L74" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L75" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>