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<Task>
</Task>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 5.1 Heat Conduction in a Rectangular Slab</Font></Text-field>
</Input>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart;</Text-field>
</Input>
</Group>
<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>
</Input>
<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>
</Input>
<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:=10;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTkc2IiIjNQ==">IiM1</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="PkkmZHlkeGJHNiIsJCooIyIiIiIiI0YoLCgtJkkidUdGJDYjIiIqNiNJInRHRiRGKComIiIkRigtJkYtNiMiIzZGMEYoRigqJiIiJUYoLSZGLTYjIiM1RjBGKCEiIkYoSSJoR0YkRj5GKA==">LCQqJiwoLSZJInVHNiI2IyIiKjYjSSJ0R0YoIiIiLSZGJzYjIiM2RisiIiQtJkYnNiMiIzVGKyEiJUYtSSJoR0YoISIiI0YtIiIj</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="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="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="PkkkYmMyRzYiLSZJInVHRiQ2IyIjNjYjSSJ0R0Yk">LSZJInVHNiI2IyIjNjYjSSJ0R0Yl</Equation></Text-field>
</Output>
</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="PiZJI2VxRzYiNiMiIzYtJkkidUdGJUYmNiNJInRHRiU=">LSZJInVHNiI2IyIjNjYjSSJ0R0Yl</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>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiYvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiMiIiVGMCIiIiomRjVGPEYtRjxGNi0mRi82IyIiJ0YwRjxGPA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiImNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIiVGLSIiIkYnRjEtJkYpNiMiIidGLUY3Rjc=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIicvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiMiIiZGMCIiIiomRjVGPEYtRjxGNi0mRi82IyIiKEYwRjxGPA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiInNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIiZGLSIiIkYnRjEtJkYpNiMiIihGLUY3Rjc=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIigvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiMiIidGMCIiIiomRjVGPEYtRjxGNi0mRi82IyIiKUYwRjxGPA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIoNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIidGLSIiIkYnRjEtJkYpNiMiIilGLUY3Rjc=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIikvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiMiIihGMCIiIiomRjVGPEYtRjxGNi0mRi82IyIiKkYwRjxGPA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIpNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIihGLSIiIkYnRjEtJkYpNiMiIipGLUY3Rjc=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiovLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiMiIilGMCIiIiomRjVGPEYtRjxGNi0mRi82IyIjNUYwRjxGPA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIqNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIilGLSIiIkYnRjEtJkYpNiMiIzVGLUY3Rjc=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiMiIipGMCIiIiomRjVGPEYtRjxGNi0mRi82IyIjNkYwRjxGPA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiM1NiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIipGLSIiIkYnRjEtJkYpNiMiIzZGLUY3Rjc=</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+1](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="Pi0mSSJ1RzYiNiMiIzY2I0kidEdGJiIiIQ==">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="PiZJI2VxRzYiNiMiIiUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiMiIiRGMCIiIiomRjVGPEYtRjxGNi0mRi82IyIiJkYwRjxGPA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIlNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIiRGLSIiIkYnRjEtJkYpNiMiIiZGLUY3Rjc=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiYvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiMiIiVGMCIiIiomRjVGPEYtRjxGNi0mRi82IyIiJ0YwRjxGPA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiImNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIiVGLSIiIkYnRjEtJkYpNiMiIidGLUY3Rjc=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIicvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiMiIiZGMCIiIiomRjVGPEYtRjxGNi0mRi82IyIiKEYwRjxGPA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiInNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIiZGLSIiIkYnRjEtJkYpNiMiIihGLUY3Rjc=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIigvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiMiIidGMCIiIiomRjVGPEYtRjxGNi0mRi82IyIiKUYwRjxGPA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIoNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIidGLSIiIkYnRjEtJkYpNiMiIilGLUY3Rjc=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIikvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiMiIihGMCIiIiomRjVGPEYtRjxGNi0mRi82IyIiKkYwRjxGPA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIpNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIihGLSIiIkYnRjEtJkYpNiMiIipGLUY3Rjc=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiovLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCgtJkYvNiMiIilGMCIiIiomRjVGPEYtRjxGNi0mRi82IyIjNUYwRjxGPA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIqNiNJInRHRipGLiomSSJoR0YqISIjLCgtJkYpNiMiIilGLSIiIkYnRjEtJkYpNiMiIzVGLUY3Rjc=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxKiYpSSJoR0YlIiIjISIiLCYtJkYvNiMiIipGMCIiIiomRjVGPEYtRjxGNkY8">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiM1NiNJInRHRipGLiomSSJoR0YqISIjLCYtJkYpNiMiIipGLSIiIkYnRjFGNw==</Equation></Text-field>
</Output>
</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="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">NywqJkkiaEc2IiEiIywmLSZJInVHRiU2IyIiIjYjSSJ0R0YlRiYtJkYqNiMiIiNGLUYsRiwqJkYkRiYsKEYoRixGL0YmLSZGKjYjIiIkRi1GLEYsKiZGJEYmLChGL0YsRjVGJi0mRio2IyIiJUYtRixGLComRiRGJiwoRjVGLEY7RiYtJkYqNiMiIiZGLUYsRiwqJkYkRiYsKEY7RixGQUYmLSZGKjYjIiInRi1GLEYsKiZGJEYmLChGQUYsRkdGJi0mRio2IyIiKEYtRixGLComRiRGJiwoRkdGLEZNRiYtJkYqNiMiIilGLUYsRiwqJkYkRiYsKEZNRixGU0YmLSZGKjYjIiIqRi1GLEYsKiZGJEYmLChGU0YsRllGJi0mRio2IyIjNUYtRixGLComRiRGJiwmRllGLEZpbkYmRiw=</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="PkkiWUc2IjcsLSZJInVHRiQ2IyIiIjYjSSJ0R0YkLSZGKDYjIiIjRistJkYoNiMiIiRGKy0mRig2IyIiJUYrLSZGKDYjIiImRistJkYoNiMiIidGKy0mRig2IyIiKEYrLSZGKDYjIiIpRistJkYoNiMiIipGKy0mRig2IyIjNUYr">NywtJkkidUc2IjYjIiIiNiNJInRHRiYtJkYlNiMiIiNGKS0mRiU2IyIiJEYpLSZGJTYjIiIlRiktJkYlNiMiIiZGKS0mRiU2IyIiJ0YpLSZGJTYjIiIoRiktJkYlNiMiIilGKS0mRiU2IyIiKkYpLSZGJTYjIiM1Rik=</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="PkkiQUc2Ii1JJ21hdHJpeEdGJDYjNyw3LCwkKiYiIiMiIiIpSSJoR0YkRiwhIiJGMCokRi5GMCIiIUYyRjJGMkYyRjJGMkYyNyxGMUYqRjFGMkYyRjJGMkYyRjJGMjcsRjJGMUYqRjFGMkYyRjJGMkYyRjI3LEYyRjJGMUYqRjFGMkYyRjJGMkYyNyxGMkYyRjJGMUYqRjFGMkYyRjJGMjcsRjJGMkYyRjJGMUYqRjFGMkYyRjI3LEYyRjJGMkYyRjJGMUYqRjFGMkYyNyxGMkYyRjJGMkYyRjJGMUYqRjFGMjcsRjJGMkYyRjJGMkYyRjJGMUYqRjE3LEYyRjJGMkYyRjJGMkYyRjJGMUYq">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L68" 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="PkkiaEc2IiMiIiIiIzY=">IyIiIiIjNg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L69" 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="PkkiQUc2Ii1JJ21hdHJpeEdGJDYjNyw3LCEkVSMiJEAiIiIhRixGLEYsRixGLEYsRiw3LEYrRipGK0YsRixGLEYsRixGLEYsNyxGLEYrRipGK0YsRixGLEYsRixGLDcsRixGLEYrRipGK0YsRixGLEYsRiw3LEYsRixGLEYrRipGK0YsRixGLEYsNyxGLEYsRixGLEYrRipGK0YsRixGLDcsRixGLEYsRixGLEYrRipGK0YsRiw3LEYsRixGLEYsRixGLEYrRipGK0YsNyxGLEYsRixGLEYsRixGLEYrRipGKzcsRixGLEYsRixGLEYsRixGLEYrRio=">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L70" 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 using the 'map(A,evalf)' 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="LUknbWF0cml4RzYiNiM3LDcsJCEkVSMiIiEkIiRAIkYqJEYqRipGLUYtRi1GLUYtRi1GLTcsRitGKEYrRi1GLUYtRi1GLUYtRi03LEYtRitGKEYrRi1GLUYtRi1GLUYtNyxGLUYtRitGKEYrRi1GLUYtRi1GLTcsRi1GLUYtRitGKEYrRi1GLUYtRi03LEYtRi1GLUYtRitGKEYrRi1GLUYtNyxGLUYtRi1GLUYtRitGKEYrRi1GLTcsRi1GLUYtRi1GLUYtRitGKEYrRi03LEYtRi1GLUYtRi1GLUYtRitGKEYrNyxGLUYtRi1GLUYtRi1GLUYtRitGKA==">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L71" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution is obtained by finding 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="L72" 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="LUknbWF0cml4RzYiNiM3LDcjJCIiIiIiIUYnRidGJ0YnRidGJ0YnRidGJw==">PTYiNiQ7IiIiIiM1O0YmRiZFXFtsKzYkIiImRiYkRiYiIiE2JEYnRiZGLDYkIiInRiZGLDYkIiIoRiZGLDYkIiIqRiZGLDYkRiZGJkYsNiQiIiNGJkYsNiQiIiVGJkYsNiQiIiRGJkYsNiQiIilGJkYs</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="PkkiWUc2Ii1JJ21hdHJpeEdGJDYjNyw3Iyw2KiYkIiUiZiUhIzYiIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiYkIisnKkgoPnUlISIoRi9JInRHRiRGLyEiIkYvRi8qJiQiKyc9NmopR0YuRi8tRjE2IywkKiYkIitcTiRlWCVGOkYvRjtGL0Y8Ri9GLyomJCIlPkEhIzVGLy1GMTYjLCQqJiQiK3dIdy9TRjpGL0Y7Ri9GPEYvRjwqJiQiK3N1KUcxIkZJRi8tRjE2IywkKiYkIitKVklETUY6Ri9GO0YvRjxGL0YvKiYkIiUsaEZJRi8tRjE2IywkKiYkIis0PlNrRkY6Ri9GO0YvRjxGL0Y8KiYkIislUUlwMiNGSUYvLUYxNiMsJComJCIrIjQpZnY/RjpGL0Y7Ri9GPEYvRi8qJiQiJSZmIkZJRi8tRjE2IywkKiYkIitwY3A5OUY6Ri9GO0YvRjxGL0YvKiYkIismcFApM0lGSUYvLUYxNiMsJComJCIrUi1QXyQpISIpRi9GO0YvRjxGL0YvKiYkIiVnOEYuRi8tRjE2IywkKiYkIiswWG1UUUZncEYvRjtGL0Y8Ri9GPComJCIrJ2Y5RmMkRklGLy1GMTYjLCQqJiQiKyZRK0YhKSohIipGL0Y7Ri9GPEYvRi83Iyw2KiYkIiU3ckYuRi9GMEYvRi8qJiQiKmwlPmNbRklGL0ZARi9GPComJCIlLVdGSUYvRkpGL0Y8KiYkIiorRjEkKSlGSUYvRlNGL0Y8KiYkIiYnKTQiRklGL0ZmbkYvRjwqJiQiKkZtOSJmRklGL0Zfb0YvRi8qJiQiJVlJRklGL0Zob0YvRi8qJiQiK2gjUjIlUkZJRi9GYXBGL0YvKiYkIiQ6JEZJRi9GW3FGL0Y8KiYkIitWIyp6T29GSUYvRmRxRi9GLzcjLDYqJiQiJGgnRklGL0YwRi9GLyomJCIqQGxWRyZGSUYvRkBGL0YvKiYkIiUtbEZJRi9GSkYvRjwqJiQiKk4yPUgkRklGL0ZTRi9GPComJCImcFIiRklGL0ZmbkYvRjwqJiQiK1YvcDM+RklGL0Zfb0YvRjwqJiQiJTdWRklGL0Zob0YvRi8qJiQiKz5JVl9ARklGL0ZhcEYvRi8qJiQiJF0mRklGL0ZbcUYvRjwqJiQiKyozMnFiKkZJRi9GZHFGL0YvNyMsNiomJCIkNiVGSUYvRjBGL0YvKiYkIipuR1kuJUZJRi9GQEYvRjwqJiQiJUkiKUZJRi9GSkYvRjwqJiQiK2w6Z2M2RklGL0ZTRi9GLyomJCImWF0iRklGL0ZmbkYvRjwqJiQiKyhlVFc4IkZJRi9GX29GL0Y8KiYkIiVyYUZJRi9GaG9GL0YvKiYkIitgO2xANkZJRi9GYXBGL0Y8KiYkIiUveUYuRi9GW3FGL0Y8KiYkIisyakhdNkZqcUYvRmRxRi9GLzcjLDYqJiQiJCI9RklGL0YwRi9GLyomJCIqIno6LzpGSUYvRkBGL0YvKiYkIiVMKilGSUYvRkpGL0Y8KiYkIipDQXFKJ0ZJRi9GU0YvRjwqJiQiJiN5OUZJRi9GZm5GL0Y8KiYkIiszV3cmZSJGSUYvRl9vRi9GLyomJCIldWpGSUYvRmhvRi9GLyomJCIrV1dbQE9GSUYvRmFwRi9GPComJCIlPSUqRi5GL0ZbcUYvRjwqJiQiK1I8cV43RmpxRi9GZHFGL0YvNyMsNiomJCIkPyNGSUYvRjBGL0YvKiYkIiovalRdIkZJRi9GQEYvRi8qJiQiJVgkKkZJRi9GSkYvRjwqJiQiKlY5cUonRklGL0ZTRi9GPComJCImJW84RklGL0ZmbkYvRjwqJiQiK2lPdyZlIkZJRi9GX29GL0YvKiYkIiUnbydGSUYvRmhvRi9GLyomJCIrXVdbQE9GSUYvRmFwRi9GPComJCIlXCoqRi5GL0ZbcUYvRjwqJiQiK1Q8cV43RmpxRi9GZHFGL0YvNyMsNiomJCIkJlJGSUYvRjBGL0YvKiYkIipfOVkuJUZJRi9GQEYvRjwqJiQiJUMnKkZJRi9GSkYvRjwqJiQiK3ZOZ2M2RklGL0ZTRi9GLyomJCImJyk+IkZJRi9GZm5GL0Y8KiYkIit3T1dNNkZJRi9GX29GL0Y8KiYkIiUnSCdGSUYvRmhvRi9GLyomJCIrVjtsQDZGSUYvRmFwRi9GPComJCIkUSpGSUYvRltxRi9GPComJCIrOGpIXTZGanFGL0ZkcUYvRi83Iyw2KiYkIiVrVkYuRi9GMEYvRi8qJiQiKlQlUSVHJkZJRi9GQEYvRi8qJiQiJVIpKUZJRi9GSkYvRjwqJiQiKiUqejxIJEZJRi9GU0YvRjwqJiQiJXIoKkZJRi9GZm5GL0Y8KiYkIit6THAzPkZJRi9GX29GL0Y8KiYkIiUqUiZGSUYvRmhvRi9GLyomJCIrITNMQzojRklGL0ZhcEYvRi8qJiQiJHUoRklGL0ZbcUYvRjwqJiQiK3ByK2QmKkZJRi9GZHFGL0YvNyMsNiomJCIlL0hGLkYvRjBGL0YvKiYkIip1d2gmW0ZJRi9GQEYvRjwqJiQiJTZtRklGL0ZKRi9GPComJCIqLSpmSSkpRklGL0ZTRi9GPComJCImcCZwRi5GL0ZmbkYvRjwqJiQiKmpPOSJmRklGL0Zfb0YvRi8qJiQiJV5TRklGL0Zob0YvRi8qJiQiK1ckUjIlUkZJRi9GYXBGL0YvKiYkIiVWYUYuRi9GW3FGL0Y8KiYkIitAJCp6T29GSUYvRmRxRi9GLzcjLDYqJiQiJVU2Ri5GL0YwRi9GLyomJCIqKj1LJylHRklGL0ZARi9GLyomJCIlKlEkRklGL0ZKRi9GPComJCIrZyQqKUcxIkZJRi9GU0YvRi8qJiQiJVRPRklGL0ZmbkYvRjwqJiQiKyNbR3AyI0ZJRi9GX29GL0YvKiYkIiUsQUZJRi9GaG9GL0YvKiYkIitaeCQpM0lGSUYvRmFwRi9GLyomJCIlIXojRi5GL0ZbcUYvRjwqJiQiK1RZcmlORklGL0ZkcUYvRi8=">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L73" 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="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErJypIKD51JSEiKCQiJSJmJSEjNi1GJDYjLCRGKyQhK1xOJGVYJUYuJCIrJz02ailHRjEtRiQ2IywkRiskISt3SHcvU0YuJCElPkEhIzUtRiQ2IywkRiskIStKVklETUYuJCIrc3UpRzEiRkAtRiQ2IywkRiskISs0PlNrRkYuJCElLGhGQC1GJDYjLCRGKyQhKyI0KWZ2P0YuJCIrJVFJcDIjRkAtRiQ2IywkRiskIStwY3A5OUYuJCIlJmYiRkAtRiQ2IywkRiskIStSLVBfJCkhIikkIismcFApM0lGQC1GJDYjLCRGKyQhKzBYbVRRRlxvJCElZzhGMS1GJDYjLCRGKyQhKyZRK0YhKSohIiokIisnZjlGYyRGQA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErJypIKD51JSEiKCQiJTdyISM2LUYkNiMsJEYrJCErXE4kZVglRi4kISpsJT5jWyEjNS1GJDYjLCRGKyQhK3dIdy9TRi4kISUtV0Y5LUYkNiMsJEYrJCErSlZJRE1GLiQhKitGMSQpKUY5LUYkNiMsJEYrJCErND5Ta0ZGLiQhJicpNCJGOS1GJDYjLCRGKyQhKyI0KWZ2P0YuJCIqRm05ImZGOS1GJDYjLCRGKyQhK3BjcDk5Ri4kIiVZSUY5LUYkNiMsJEYrJCErUi1QXyQpISIpJCIraCNSMiVSRjktRiQ2IywkRiskISswWG1UUUZcbyQhJDokRjktRiQ2IywkRiskISsmUStGISkqISIqJCIrViMqek9vRjk=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErJypIKD51JSEiKCQiJGgnISM1LUYkNiMsJEYrJCErXE4kZVglRi4kIipAbFZHJkYxLUYkNiMsJEYrJCErd0h3L1NGLiQhJS1sRjEtRiQ2IywkRiskIStKVklETUYuJCEqTjI9SCRGMS1GJDYjLCRGKyQhKzQ+U2tGRi4kISZwUiJGMS1GJDYjLCRGKyQhKyI0KWZ2P0YuJCErVi9wMz5GMS1GJDYjLCRGKyQhK3BjcDk5Ri4kIiU3VkYxLUYkNiMsJEYrJCErUi1QXyQpISIpJCIrPklWX0BGMS1GJDYjLCRGKyQhKzBYbVRRRltvJCEkXSZGMS1GJDYjLCRGKyQhKyZRK0YhKSohIiokIisqMzJxYipGMQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErJypIKD51JSEiKCQiJDYlISM1LUYkNiMsJEYrJCErXE4kZVglRi4kISpuR1kuJUYxLUYkNiMsJEYrJCErd0h3L1NGLiQhJUkiKUYxLUYkNiMsJEYrJCErSlZJRE1GLiQiK2w6Z2M2RjEtRiQ2IywkRiskISs0PlNrRkYuJCEmWF0iRjEtRiQ2IywkRiskISsiNClmdj9GLiQhKyhlVFc4IkYxLUYkNiMsJEYrJCErcGNwOTlGLiQiJXJhRjEtRiQ2IywkRiskIStSLVBfJCkhIikkIStgO2xANkYxLUYkNiMsJEYrJCErMFhtVFFGW28kISUveSEjNi1GJDYjLCRGKyQhKyZRK0YhKSohIiokIisyakhdNkZbcA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErJypIKD51JSEiKCQiJCI9ISM1LUYkNiMsJEYrJCErXE4kZVglRi4kIioiejovOkYxLUYkNiMsJEYrJCErd0h3L1NGLiQhJUwqKUYxLUYkNiMsJEYrJCErSlZJRE1GLiQhKkNBcUonRjEtRiQ2IywkRiskISs0PlNrRkYuJCEmI3k5RjEtRiQ2IywkRiskISsiNClmdj9GLiQiKzNXdyZlIkYxLUYkNiMsJEYrJCErcGNwOTlGLiQiJXVqRjEtRiQ2IywkRiskIStSLVBfJCkhIikkIStXV1tAT0YxLUYkNiMsJEYrJCErMFhtVFFGW28kISU9JSohIzYtRiQ2IywkRiskISsmUStGISkqISIqJCIrUjxxXjdGW3A=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErJypIKD51JSEiKCQiJD8jISM1LUYkNiMsJEYrJCErXE4kZVglRi4kIiovalRdIkYxLUYkNiMsJEYrJCErd0h3L1NGLiQhJVgkKkYxLUYkNiMsJEYrJCErSlZJRE1GLiQhKlY5cUonRjEtRiQ2IywkRiskISs0PlNrRkYuJCEmJW84RjEtRiQ2IywkRiskISsiNClmdj9GLiQiK2lPdyZlIkYxLUYkNiMsJEYrJCErcGNwOTlGLiQiJSdvJ0YxLUYkNiMsJEYrJCErUi1QXyQpISIpJCErXVdbQE9GMS1GJDYjLCRGKyQhKzBYbVRRRltvJCElXCoqISM2LUYkNiMsJEYrJCErJlErRiEpKiEiKiQiK1Q8cV43Rltw</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErJypIKD51JSEiKCQiJCZSISM1LUYkNiMsJEYrJCErXE4kZVglRi4kISpfOVkuJUYxLUYkNiMsJEYrJCErd0h3L1NGLiQhJUMnKkYxLUYkNiMsJEYrJCErSlZJRE1GLiQiK3ZOZ2M2RjEtRiQ2IywkRiskISs0PlNrRkYuJCEmJyk+IkYxLUYkNiMsJEYrJCErIjQpZnY/Ri4kISt3T1dNNkYxLUYkNiMsJEYrJCErcGNwOTlGLiQiJSdIJ0YxLUYkNiMsJEYrJCErUi1QXyQpISIpJCErVjtsQDZGMS1GJDYjLCRGKyQhKzBYbVRRRltvJCEkUSpGMS1GJDYjLCRGKyQhKyZRK0YhKSohIiokIis4akhdNkZqbw==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErJypIKD51JSEiKCQiJWtWISM2LUYkNiMsJEYrJCErXE4kZVglRi4kIipUJVElRyYhIzUtRiQ2IywkRiskISt3SHcvU0YuJCElUikpRjktRiQ2IywkRiskIStKVklETUYuJCEqJSp6PEgkRjktRiQ2IywkRiskISs0PlNrRkYuJCElcigqRjktRiQ2IywkRiskISsiNClmdj9GLiQhK3pMcDM+RjktRiQ2IywkRiskIStwY3A5OUYuJCIlKlImRjktRiQ2IywkRiskIStSLVBfJCkhIikkIishM0xDOiNGOS1GJDYjLCRGKyQhKzBYbVRRRlxvJCEkdShGOS1GJDYjLCRGKyQhKyZRK0YhKSohIiokIitwcitkJipGOQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErJypIKD51JSEiKCQiJS9IISM2LUYkNiMsJEYrJCErXE4kZVglRi4kISp1d2gmWyEjNS1GJDYjLCRGKyQhK3dIdy9TRi4kISU2bUY5LUYkNiMsJEYrJCErSlZJRE1GLiQhKi0qZkkpKUY5LUYkNiMsJEYrJCErND5Ta0ZGLiQhJnAmcEYxLUYkNiMsJEYrJCErIjQpZnY/Ri4kIipqTzkiZkY5LUYkNiMsJEYrJCErcGNwOTlGLiQiJV5TRjktRiQ2IywkRiskIStSLVBfJCkhIikkIitXJFIyJVJGOS1GJDYjLCRGKyQhKzBYbVRRRlxvJCElVmFGMS1GJDYjLCRGKyQhKyZRK0YhKSohIiokIitAJCp6T29GOQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErJypIKD51JSEiKCQiJVU2ISM2LUYkNiMsJEYrJCErXE4kZVglRi4kIioqPUsnKUchIzUtRiQ2IywkRiskISt3SHcvU0YuJCElKlEkRjktRiQ2IywkRiskIStKVklETUYuJCIrZyQqKUcxIkY5LUYkNiMsJEYrJCErND5Ta0ZGLiQhJVRPRjktRiQ2IywkRiskISsiNClmdj9GLiQiKyNbR3AyI0Y5LUYkNiMsJEYrJCErcGNwOTlGLiQiJSxBRjktRiQ2IywkRiskIStSLVBfJCkhIikkIitaeCQpM0lGOS1GJDYjLCRGKyQhKzBYbVRRRlxvJCElIXojRjEtRiQ2IywkRiskISsmUStGISkqISIqJCIrVFlyaU5GOQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIzY2I0kidEdGJiIiIQ==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L74" 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:</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,thickness=3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 16352 characters]">[encoded data, 16324 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L83" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">arw:=arrow(&lt;0.10,0.8&gt;,&lt;-0.09,-0.6&gt;,width=[1/500,relative],head_length=[1/20,relative]):
pt:=textplot([[0.2,0.9,&quot;Follow the arrow:&quot;],seq([0.18,0.9-i*0.06,typeset(u[5-i+1],&quot;(t), &quot;,u[6+i-1],&quot;(t)&quot;)],i=1..6)]):</Text-field>
</Input>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({pp,arw,pt},axes=boxed,title=&quot;Figure Exp. 5.3&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, 61572 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L75" 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 up to which you want to plot your profiles (this time has to 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="L76" 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="L77" 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="PkkjUFBHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIzc7RioiI0o3Ig==">PTYiNiQ7IiIiIiM3O0YmIiNKRVxbbCE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L79" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The first column of PP is filled in 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 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. 5.4&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, 17488 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>
<Group labelreference="L82" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We observe that the process slowly approaches the steady state.  We note that the profiles are symmetrical about x = 0.5, and, hence, we obtain u[0]=u[n+1],u[1]=u[N}, etc.</Text-field>
</Input>
</Group>
</Worksheet>