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<Input>
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 5.1a Heat Conduction in a Rectangular Slab</Font></Text-field>
</Input>
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<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Consider the heat conduction problem in a slab.[6]  The governing equation in dimensionless form is</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="Text" input-equation="" display="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">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</Equation></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred">                                                                                         u(x,0) = 1                                                               (5.1.12)            </Text-field>
<Text-field style="Text" layout="Normal" alignment="centred">              </Text-field>
<Text-field style="Text" layout="Normal" alignment="centred">u(0,t) = 0 and u(1,t) = 0</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">This equation is solved in Maple below using the procedure described above.</Text-field>
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<Input>
<Text-field style="Text" layout="Normal"></Text-field>
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<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart;</Text-field>
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<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(linalg):with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L54" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the governing equation here:</Text-field>
</Input>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ge:=diff(u(x,t),t)=diff(u(x,t),x$2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZ2VHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkidEdGJEYuLUYnNiRGKi1JIiRHRig2JEYtIiIj">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLC1GJDYkLUYkNiRGJ0YrRis=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the boundary condition at x = 0:</Text-field>
</Input>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=u(x,t);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLUkidUdGJDYkSSJ4R0YkSSJ0R0Yk">LUkidUc2IjYkSSJ4R0YkSSJ0R0Yk</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the boundary condition at x = L:</Text-field>
</Input>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=u(x,t);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLUkidUdGJDYkSSJ4R0YkSSJ0R0Yk">LUkidUc2IjYkSSJ4R0YkSSJ0R0Yk</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L58" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the initial condition:</Text-field>
</Input>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IC:=u(x,0)=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSUNHNiIvLUkidUdGJDYkSSJ4R0YkIiIhIiIi">Ly1JInVHNiI2JEkieEdGJSIiISIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L59" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the number of interior node points:</Text-field>
</Input>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=4;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTkc2IiIiJQ==">IiIl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L60" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the length of the domain:</Text-field>
</Input>
</Group>
<Group labelreference="L10" 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="L61" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the three point backward difference expression (accurate to the order h<Font superscript="true" size="10">2</Font>) for the first derivative at x = L:</Text-field>
</Input>
</Group>
<Group labelreference="L11" 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))/h;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGZHNiIsJCooIyIiIiIiI0YoLCgtJkkidUdGJDYjRik2I0kidEdGJCEiIiomIiIkRigtJkYtNiMiIiFGL0YoRjEqJiIiJUYoLSZGLTYjRihGL0YoRihGKEkiaEdGJEYxRig=">LCQqJiwoLSZJInVHNiI2IyIiIzYjSSJ0R0YoISIiLSZGJzYjIiIhRishIiQtJkYnNiMiIiJGKyIiJUY2SSJoR0YoRi0jRjZGKg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L62" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the three point central difference expression (accurate to the order h<Font superscript="true" size="10">2</Font>) for the second derivative at x = L:</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxb:=1/2*(u[N-1](t)+3*u[N+1](t)-4*u[N](t))/h;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGJHNiIsJCooIyIiIiIiI0YoLCgtJkkidUdGJDYjIiIkNiNJInRHRiRGKComRi9GKC0mRi02IyIiJkYwRihGKComIiIlRigtJkYtNiNGOEYwRighIiJGKEkiaEdGJEY8Rig=">LCQqJiwoLSZJInVHNiI2IyIiJDYjSSJ0R0YoIiIiLSZGJzYjIiImRitGKi0mRic2IyIiJUYrISIlRi1JImhHRighIiIjRi0iIiM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L63" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Convert the boundary conditions to the finite difference form:</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydx:=1/2/h*(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="PkklZHlkeEc2IiwkKigjIiIiIiIjRihJImhHRiQhIiIsJi0mSSJ1R0YkNiMsJkkibUdGJEYoRihGKDYjSSJ0R0YkRigtJkYvNiMsJkYyRihGKEYrRjNGK0YoRig=">LCQqJkkiaEc2IiEiIiwmLSZJInVHRiU2IywmSSJtR0YlIiIiRi5GLjYjSSJ0R0YlRi4tJkYqNiMsJkYtRi5GJkYuRi9GJkYuI0YuIiIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">d2ydx2:=1/h^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="PkknZDJ5ZHgyRzYiKiYpSSJoR0YkIiIjISIiLCgtJkkidUdGJDYjLCZJIm1HRiQiIiJGMUYpNiNJInRHRiRGMSomRihGMS0mRi02I0YwRjJGMUYpLSZGLTYjLCZGMEYxRjFGMUYyRjFGMQ==">KiZJImhHNiIhIiMsKC0mSSJ1R0YkNiMsJkkibUdGJCIiIiEiIkYtNiNJInRHRiRGLS0mRik2I0YsRi9GJS0mRik2IywmRixGLUYtRi1GL0YtRi0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=subs(diff(u(x,t),x)=dydxf,u(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="PkkkYmMxRzYiLSZJInVHRiQ2IyIiITYjSSJ0R0Yk">LSZJInVHNiI2IyIiITYjSSJ0R0Yl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=subs(diff(u(x,t),x)=dydxb,u(x,t)=u[N+1](t),x=1,bc2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLSZJInVHRiQ2IyIiJjYjSSJ0R0Yk">LSZJInVHNiI2IyIiJjYjSSJ0R0Yl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L64" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The boundary conditions are stored in eq[0] and eq[N+1].</Text-field>
</Input>
</Group>
<Group labelreference="L17" 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="PiZJI2VxRzYiNiMiIiEtJkkidUdGJUYmNiNJInRHRiU=">LSZJInVHNiI2IyIiITYjSSJ0R0Yl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[N+1]:=bc2; </Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiYtJkkidUdGJUYmNiNJInRHRiU=">LSZJInVHNiI2IyIiJjYjSSJ0R0Yl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L65" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The governing equations are converted to the finite difference form:</Text-field>
</Input>
</Group>
<Group labelreference="L19" 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(u(x,t),x$2) = subs(m=i,d2ydx2),diff(u(x,t),x) = subs(m=i,dydx),u(x,t)=u[i](t),x=i*h,rhs(ge));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiMiIiFGMEYnKiZGNUYnRi1GJ0Y2LSZGLzYjRjVGMEYnRic=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIiNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIiFGLUYsRidGMS0mRik2IyIiI0YtRixGLA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlRichIiIsKC0mRi82IyIiIkYwRjoqJkYnRjpGLUY6RjUtJkYvNiMiIiRGMEY6Rjo=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIjNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIiJGLUY2RidGMS0mRik2IyIiJEYtRjZGNg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiNGNUYwIiIiKiZGNUY7Ri1GO0Y2LSZGLzYjIiIlRjBGO0Y7">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIkNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIiNGLSIiIkYnRjEtJkYpNiMiIiVGLUY3Rjc=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiMiIiRGMCIiIiomRjVGPEYtRjxGNi0mRi82IyIiJkYwRjxGPA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIlNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIiRGLSIiIkYnRjEtJkYpNiMiIiZGLUY3Rjc=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L66" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The boundary values u[0](t) and u[N+0](t) are eliminated:</Text-field>
</Input>
</Group>
<Group labelreference="L20" 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="Pi0mSSJ1RzYiNiMiIiE2I0kidEdGJkYo">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" 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="Pi0mSSJ1RzYiNiMiIiY2I0kidEdGJiIiIQ==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L67" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The governing equations are simplified as:</Text-field>
</Input>
</Group>
<Group labelreference="L22" 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;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCYqJkY1RidGLUYnRjYtJkYvNiNGNUYwRidGJw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIiNiNJInRHRipGLiomSSJoR0YqISIjLCZGJ0YxLSZGKTYjIiIjRi1GLEYs</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlRichIiIsKC0mRi82IyIiIkYwRjoqJkYnRjpGLUY6RjUtJkYvNiMiIiRGMEY6Rjo=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIjNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIiJGLUY2RidGMS0mRik2IyIiJEYtRjZGNg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiNGNUYwIiIiKiZGNUY7Ri1GO0Y2LSZGLzYjIiIlRjBGO0Y7">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIkNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIiNGLSIiIkYnRjEtJkYpNiMiIiVGLUY3Rjc=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCYtJkYvNiMiIiRGMCIiIiomRjVGPEYtRjxGNkY8">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIlNiNJInRHRipGLiomSSJoR0YqISIjLCYtJkYpNiMiIiRGLSIiIkYnRjFGNw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L68" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The coefficient matrix (<Font bold="true">A</Font>) is generated using Maple's 'genmatrix' command.</Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=[seq(rhs(eq[j]),j=1..N)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFzRzYiNyYqJilJImhHRiQiIiMhIiIsJiomRikiIiItJkkidUdGJDYjRi02I0kidEdGJEYtRiotJkYwNiNGKUYyRi1GLSomRidGKiwoRi5GLSomRilGLUY0Ri1GKi0mRjA2IyIiJEYyRi1GLSomRidGKiwoRjRGLSomRilGLUY6Ri1GKi0mRjA2IyIiJUYyRi1GLSomRidGKiwmRjpGLSomRilGLUZBRi1GKkYt">NyYqJkkiaEc2IiEiIywmLSZJInVHRiU2IyIiIjYjSSJ0R0YlRiYtJkYqNiMiIiNGLUYsRiwqJkYkRiYsKEYoRixGL0YmLSZGKjYjIiIkRi1GLEYsKiZGJEYmLChGL0YsRjVGJi0mRio2IyIiJUYtRixGLComRiRGJiwmRjVGLEY7RiZGLA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=[seq(u[i](t),i=1..N)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiWUc2IjcmLSZJInVHRiQ2IyIiIjYjSSJ0R0YkLSZGKDYjIiIjRistJkYoNiMiIiRGKy0mRig2IyIiJUYr">NyYtJkkidUc2IjYjIiIiNiNJInRHRiYtJkYlNiMiIiNGKS0mRiU2IyIiJEYpLSZGJTYjIiIlRik=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=genmatrix(eqs,Y);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQUc2Ii1JJ21hdHJpeEdGJDYjNyY3JiwkKiYiIiMiIiIpSSJoR0YkRiwhIiJGMCokRi5GMCIiIUYyNyZGMUYqRjFGMjcmRjJGMUYqRjE3JkYyRjJGMUYq">PTYiNiQ7IiIiIiIlRiVFXFtsMTYkIiIjIiIkKiRJImhHRiMhIiM2JEYnRioiIiE2JEYnRitGLDYkRitGJkYwNiRGJ0YnLCRGLEYuNiRGK0YqRiw2JEYnRiZGMDYkRipGJ0YwNiRGJkYqRiw2JEYrRidGLDYkRiZGJkY0NiRGKkYmRiw2JEYrRitGNDYkRiZGK0YwNiRGKkYqRjQ2JEYmRidGMA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L69" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The node spacing, h, is evaluated here:</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">h:=eval(1/(N+1));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiaEc2IiMiIiIiIiY=">IyIiIiIiJg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L70" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The <Font bold="true">A</Font> matrix is simplified as:</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=map(eval,A);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQUc2Ii1JJ21hdHJpeEdGJDYjNyY3JiEjXSIjRCIiIUYsNyZGK0YqRitGLDcmRixGK0YqRis3JkYsRixGK0Yq">PTYiNiQ7IiIiIiIlRiVFXFtsMTYkIiIjIiIkIiNENiRGJ0YqIiIhNiRGJ0YrRiw2JEYrRiZGLjYkRidGJyEjXTYkRitGKkYsNiRGJ0YmRi42JEYqRidGLjYkRiZGKkYsNiRGK0YnRiw2JEYmRiZGMjYkRipGJkYsNiRGK0YrRjI2JEYmRitGLjYkRipGKkYyNiRGJkYnRi4=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L71" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">When more than four node points are used, the entries of the <Font bold="true">A</Font> matrix should be decimals.  This problem can be handled by using the 'map(A,evalf)' command as given below:</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">if N &gt; 4 then A:=map(evalf,A);end: </Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalm(A);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUknbWF0cml4RzYiNiM3JjcmISNdIiNEIiIhRio3JkYpRihGKUYqNyZGKkYpRihGKTcmRipGKkYpRig=">PTYiNiQ7IiIiIiIlRiVFXFtsMTYkIiIjIiIkIiNENiRGJ0YqIiIhNiRGJ0YrRiw2JEYrRiZGLjYkRidGJyEjXTYkRitGKkYsNiRGJ0YmRi42JEYqRidGLjYkRiZGKkYsNiRGK0YnRiw2JEYmRiZGMjYkRipGJkYsNiRGK0YrRjI2JEYmRitGLjYkRipGKkYyNiRGJkYnRi4=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L72" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution is found using the exponential matrix:</Text-field>
</Input>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=exponential(A,t):</Text-field>
</Input>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=map(evalf,mat):</Text-field>
</Input>
</Group>
<Group labelreference="L73" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The initial condition is stored in the Y0 vector.</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y0:=matrix(N,1):for i from 1 to N do Y0[i,1]:=evalf(subs(x=i*h,rhs(IC)));od:evalm(Y0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUknbWF0cml4RzYiNiM3JjcjJCIiIiIiIUYnRidGJw==">PTYiNiQ7IiIiIiIlO0YmRiZFXFtsJTYkIiIkRiYkRiYiIiE2JEYnRiZGLDYkRiZGJkYsNiQiIiNGJkYs</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=evalm(mat&amp;*Y0):</Text-field>
</Input>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=map(simplify,Y);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiWUc2Ii1JJ21hdHJpeEdGJDYjNyY3IywmKiYkIisjKXoxT3MhIzUiIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiYkIispR10iXCYqISIqRi9JInRHRiRGLyEiIkYvRi8qJiQiK0E/JFJ3I0YuRi8tRjE2IywkKiYkIityXDNYbCEiKUYvRjtGL0Y8Ri9GLzcjLCYqJiQiKyVSPzM8IkY6Ri9GMEYvRi8qJiQiK01SPzM8Ri5GL0ZARi9GPEZHRik=">PTYiNiQ7IiIiIiIlO0YmRiZFXFtsJTYkIiIkRiYsJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGIzYjLCRJInRHRiMkISspR10iXCYqISIqJCIrJVI/MzwiRjctRi42IywkRjQkIStyXDNYbCEiKSQhK01SPzM8ISM1NiRGJ0YmLCZGLSQiKyMpejFPc0ZCRjokIitBPyRSdyNGQjYkRiZGJkZENiQiIiNGJkYs</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L74" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, the dependent variables can be stored in u<Font subscript="true">i</Font>(t),i = 0..N+1.</Text-field>
</Input>
</Group>
<Group labelreference="L35" 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="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 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="Pi0mSSJ1RzYiNiMiIiE2I0kidEdGJkYo">IiIh</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiI2I0kidEdGJiwmKiYkIisjKXoxT3MhIzVGKC1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjLCQqJiQiKylHXSJcJiohIipGKEYqRighIiJGKEYoKiYkIitBPyRSdyNGL0YoLUYxNiMsJComJCIrclwzWGwhIilGKEYqRihGO0YoRig=">LCYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErKUddIlwmKiEiKiQiKyMpejFPcyEjNS1GJDYjLCRGKyQhK3JcM1hsISIpJCIrQT8kUncjRjE=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiM2I0kidEdGJiwmKiYkIislUj8zPCIhIioiIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IywkKiYkIispR10iXCYqRi9GMEYqRjAhIiJGMEYwKiYkIitNUj8zPCEjNUYwLUYyNiMsJComJCIrclwzWGwhIilGMEYqRjBGO0YwRjs=">LCYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErKUddIlwmKiEiKiQiKyVSPzM8IkYuLUYkNiMsJEYrJCErclwzWGwhIikkIStNUj8zPCEjNQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiQ2I0kidEdGJiwmKiYkIislUj8zPCIhIioiIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IywkKiYkIispR10iXCYqRi9GMEYqRjAhIiJGMEYwKiYkIitNUj8zPCEjNUYwLUYyNiMsJComJCIrclwzWGwhIilGMEYqRjBGO0YwRjs=">LCYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErKUddIlwmKiEiKiQiKyVSPzM8IkYuLUYkNiMsJEYrJCErclwzWGwhIikkIStNUj8zPCEjNQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiU2I0kidEdGJiwmKiYkIisjKXoxT3MhIzUiIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IywkKiYkIispR10iXCYqISIqRjBGKkYwISIiRjBGMComJCIrQT8kUncjRi9GMC1GMjYjLCQqJiQiK3JcM1hsISIpRjBGKkYwRjxGMEYw">LCYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErKUddIlwmKiEiKiQiKyMpejFPcyEjNS1GJDYjLCRGKyQhK3JcM1hsISIpJCIrQT8kUncjRjE=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiY2I0kidEdGJiIiIQ==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L75" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Hence, an analytical solution in time is obtained for the dependent variables at all of the node points.  One can plot the concentration profiles by using 'seq' to assign color autolmaticly for every curve.</Text-field>
</Input>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pp:=plot([seq(u[i](t),i=0..N+1)],t=0..0.4);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 4788 characters]">[encoded data, 4760 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L83" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pt:=textplot([[0.05,0.05,typeset(u[0],&quot;(t), &quot;,u[5],&quot;(t)&quot;)],[0.1,0.2,typeset(u[1],&quot;(t), &quot;,u[4],&quot;(t)&quot;)],[0.15,0.4,typeset(u[2],&quot;(t), &quot;,u[3],&quot;(t)&quot;)]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjcHRHNiItSS9JTlRFUkZBQ0VfUExPVEdGJDYlLUklVEVYVEdGJDYkNyQkIiImISIjRiwtSSlfVFlQRVNFVEdGJDYmJkkidUdGJDYjIiIhUSYodCksfkYkJkYzNiNGLVEkKHQpRiQtRik2JDckJCIiIiEiIiQiIiNGPy1GMDYmJkYzNiNGPkY2JkYzNiMiIiVGOS1GKTYkNyQkIiM6Ri4kRkhGPy1GMDYmJkYzNiNGQUY2JkYzNiMiIiRGOQ==">LSUlUExPVEc2JS1JJVRFWFRHNiI2JDckJCIiJiEiI0YqLUkpX1RZUEVTRVRHRic2JiZJInVHRic2IyIiIVEmKHQpLH5GJyZGMTYjRitRJCh0KUYnLUYmNiQ3JCQiIiIhIiIkIiIjRj0tRi42JiZGMTYjRjxGNCZGMTYjIiIlRjctRiY2JDckJCIjOkYsJEZGRj0tRi42JiZGMTYjRj9GNCZGMTYjIiIkRjc=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({pp,pt},axes=boxed,thickness=4,title=&quot;Figure Exp. 5.1.&quot;,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, 25352 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L76" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">A three dimensional plot can be made by storing the solution in a matrix (PP).  Enter the time that you want to use to plot your profiles (this time can be changed depending on the problem):</Text-field>
</Input>
</Group>
<Group labelreference="L39" 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="L77" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the number of time steps (excluding 0):</Text-field>
</Input>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">M:=30;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTUc2IiIjSQ==">IiNJ</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L78" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The time intervals are stored in T1:</Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T1:=[seq(tf*i/M,i=0..M)];</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="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">PP:=matrix(N+2,M+1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjUFBHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIic7RioiI0o3Ig==">PTYiNiQ7IiIiIiInO0YmIiNKRVxbbCE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L79" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The first column of PP is filled by using the initial condition:</Text-field>
</Input>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N+2 do PP[i,1]:=evalf(subs(x=(i-1)*h,rhs(IC)));od:</Text-field>
</Input>
</Group>
<Group labelreference="L80" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The remaining columns are filled in by using the solution obtained:</Text-field>
</Input>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N+2 do for j from 2 to M+1 do PP[i,j]:=evalf(subs(t=T1[j],u[i-1](t)));od;od:</Text-field>
</Input>
</Group>
<Group labelreference="L81" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, data points are stored in plotdata for obtaining a 3D plot using Maple's 'surfdata' command.</Text-field>
</Input>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plotdata := [seq([ seq([(i-1)*h,T1[j],PP[i,j]], i=1..N+2)], j=1..M+1)]:</Text-field>
</Input>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">surfdata( plotdata, axes=boxed, title=&quot;Figure Exp. 5.2.&quot;,labels=[x,t,u],orientation=[45,60]);</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, 8552 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>