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<Group labelreference="L55" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Example 5.2.5 Two Coupled PDEs</Text-field>
</Input>
</Group>
<Group labelreference="L54" 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="L57" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the governing equations:</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ge[1]:=diff(u[1](x,t),t)=diff((u[2](x,t)-1)*diff(u[1](x,t),x),x)+(16*x*t-2*t-16*(u[2](x,t)-1))*(u[1](x,t)-1)+10*x*exp(-4*x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2dlRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2JEkieEdGJUkidEdGJUYyLCoqJi1GKjYkLSZGLzYjIiIjRjBGMUYnLUYqNiRGLUYxRidGJyomLCZGN0YnRichIiJGJy1GKjYkRi0tSSIkR0YrNiRGMUY6RidGJyomLCoqKCIjO0YnRjFGJ0YyRidGJyomRjpGJ0YyRidGPyomRkhGJ0Y3RidGP0ZIRidGJywmRi1GJ0YnRj9GJ0YnKigiIzVGJ0YxRictSSRleHBHNiRGK0koX3N5c2xpYkdGJTYjLCQqJiIiJUYnRjFGJ0Y/RidGJw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIiNiRJInhHRipJInRHRipGLywqKiYtRiQ2JC0mRik2IyIiI0YtRi5GLC1GJDYkRidGLkYsRiwqJiwmRjRGLCEiIkYsRiwtRiQ2JEY4Ri5GLEYsKiYsKiomRi5GLEYvRiwiIztGLyEiI0Y0ISM7RkJGLEYsLCZGJ0YsRjxGLEYsRiwqJkYuRiwtSSRleHBHNiRGJUkoX3N5c2xpYkdGKjYjLCRGLiEiJUYsIiM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ge[2]:=diff(u[2](x,t),t)=diff(u[2](x,t),x$2)+diff(u[1](x,t),x)+4*(u[1](x,t)-1)+x^2-2*t-10*t*exp(-4*x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2dlRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2JEkieEdGJUkidEdGJUYyLDAtRio2JEYtLUkiJEdGKzYkRjFGJyIiIi1GKjYkLSZGLzYjRjlGMEYxRjkqJiIiJUY5RjxGOUY5RkAhIiIqJClGMUYnRjlGOSomRidGOUYyRjlGQSooIiM1RjlGMkY5LUkkZXhwRzYkRitJKF9zeXNsaWJHRiU2IywkKiZGQEY5RjFGOUZBRjlGQQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIjNiRJInhHRipJInRHRipGLywwLUYkNiQtRiQ2JEYnRi5GLiIiIi1GJDYkLSZGKTYjRjVGLUYuRjVGOCIiJSEiJUY1KiRGLkYsRjVGLyEiIyomRi9GNS1JJGV4cEc2JEYlSShfc3lzbGliR0YqNiMsJEYuRjxGNSEjNQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L58" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the boundary conditions at x = 0:</Text-field>
</Input>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1[1]:=u[1](x,t)-1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJGJjMUc2IjYjIiIiLCYtJkkidUdGJUYmNiRJInhHRiVJInRHRiVGJ0YnISIi">LCYtJkkidUc2IjYjIiIiNiRJInhHRiZJInRHRiZGKCEiIkYo</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1[2]:=u[2](x,t)-1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJGJjMUc2IjYjIiIjLCYtJkkidUdGJUYmNiRJInhHRiVJInRHRiUiIiJGLyEiIg==">LCYtJkkidUc2IjYjIiIjNiRJInhHRiZJInRHRiYiIiIhIiJGLA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L59" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the boundary conditions at x = 1:</Text-field>
</Input>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2[1]:=3*u[1](x,t)+diff(u[1](x,t),x)-3;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJGJjMkc2IjYjIiIiLCgqJiIiJEYnLSZJInVHRiVGJjYkSSJ4R0YlSSJ0R0YlRidGJy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiRGK0YvRidGKiEiIg==">LCgtJkkidUc2IjYjIiIiNiRJInhHRiZJInRHRiYiIiQtSSVkaWZmRyUqcHJvdGVjdGVkRzYkRiNGKkYoISIkRig=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2[2]:=5*diff(u[2](x,t),x)-evalf(exp(4))*(u[1](x,t)-1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJGJjMkc2IjYjIiIjLCgqJiIiJiIiIi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUdGJUYmNiRJInhHRiVJInRHRiVGNEYrRisqJiQiKy5dIilmYSEiKUYrLSZGMjYjRitGM0YrISIiRjdGKw==">LCgtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJInVHNiI2IyIiIzYkSSJ4R0YqSSJ0R0YqRi4iIiYtJkYpNiMiIiJGLSQhKy5dIilmYSEiKSQiKy5dIilmYUY3RjQ=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L60" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the initial conditions:</Text-field>
</Input>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IC[1]:=u[1](x,0)=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0lDRzYiNiMiIiIvLSZJInVHRiVGJjYkSSJ4R0YlIiIhRic=">Ly0mSSJ1RzYiNiMiIiI2JEkieEdGJiIiIUYo</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IC[2]:=u[2](x,0)=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0lDRzYiNiMiIiMvLSZJInVHRiVGJjYkSSJ4R0YlIiIhIiIi">Ly0mSSJ1RzYiNiMiIiM2JEkieEdGJiIiISIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L61" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the number of governing equations:</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">NN:=2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjTk5HNiIiIiM=">IiIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTkc2IiIiIw==">IiIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" 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="L62" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Develop finite difference expressions for the first and second derivatives for the given two dependent dependent variables:</Text-field>
</Input>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to NN do </Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxf[i]:=1/2*(-u[2,i](t)-3*u[0,i](t)+4*u[1,i](t))/h;</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxb[i]:=1/2*(u[N-1,i](t)+3*u[N+1,i](t)-4*u[N,i](t))/h;</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydx[i]:=1/2/h*(u[m+1,i](t)-u[m-1,i](t));</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">d2ydx2[i]:=1/h^2*(u[m-1,i](t)-2*u[m,i](t)+u[m+1,i](t));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJmR5ZHhmRzYiNiMiIiIsJCooI0YnIiIjRicsKC0mSSJ1R0YlNiRGK0YnNiNJInRHRiUhIiIqJiIiJEYnLSZGLzYkIiIhRidGMUYnRjMqJiIiJUYnLSZGLzYkRidGJ0YxRidGJ0YnSSJoR0YlRjNGJw==">LCQqJiwoLSZJInVHNiI2JCIiIyIiIjYjSSJ0R0YoISIiLSZGJzYkIiIhRitGLCEiJC0mRic2JEYrRitGLCIiJUYrSSJoR0YoRi4jRitGKg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJmR5ZHhiRzYiNiMiIiIsJCooI0YnIiIjRicsKC0mSSJ1R0YlNiRGJ0YnNiNJInRHRiVGJyomIiIkRictJkYvNiRGNEYnRjFGJ0YnKiYiIiVGJy0mRi82JEYrRidGMUYnISIiRidJImhHRiVGPUYn">LCQqJiwoLSZJInVHNiI2JCIiIkYqNiNJInRHRihGKi0mRic2JCIiJEYqRitGMC0mRic2JCIiI0YqRishIiVGKkkiaEdGKCEiIiNGKkY0</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJWR5ZHhHNiI2IyIiIiwkKigjRiciIiNGJ0kiaEdGJSEiIiwmLSZJInVHRiU2JCwmSSJtR0YlRidGJ0YnRic2I0kidEdGJUYnLSZGMTYkLCZGNEYnRidGLUYnRjVGLUYnRic=">LCQqJkkiaEc2IiEiIiwmLSZJInVHRiU2JCwmSSJtR0YlIiIiRi5GLkYuNiNJInRHRiVGLi0mRio2JCwmRi1GLkYmRi5GLkYvRiZGLiNGLiIiIw==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJ2QyeWR4Mkc2IjYjIiIiKiYpSSJoR0YlIiIjISIiLCgtJkkidUdGJTYkLCZJIm1HRiVGJ0YnRixGJzYjSSJ0R0YlRicqJkYrRictJkYwNiRGM0YnRjRGJ0YsLSZGMDYkLCZGM0YnRidGJ0YnRjRGJ0Yn">KiZJImhHNiIhIiMsKC0mSSJ1R0YkNiQsJkkibUdGJCIiIiEiIkYtRi02I0kidEdGJEYtLSZGKTYkRixGLUYvRiUtJkYpNiQsJkYsRi1GLUYtRi1GL0YtRi0=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJmR5ZHhmRzYiNiMiIiMsJCooIyIiIkYnRissKC0mSSJ1R0YlNiRGJ0YnNiNJInRHRiUhIiIqJiIiJEYrLSZGLzYkIiIhRidGMUYrRjMqJiIiJUYrLSZGLzYkRitGJ0YxRitGK0YrSSJoR0YlRjNGKw==">LCQqJiwoLSZJInVHNiI2JCIiI0YqNiNJInRHRighIiItJkYnNiQiIiFGKkYrISIkLSZGJzYkIiIiRipGKyIiJUY2SSJoR0YoRi0jRjZGKg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJmR5ZHhiRzYiNiMiIiMsJCooIyIiIkYnRissKC0mSSJ1R0YlNiRGK0YnNiNJInRHRiVGKyomIiIkRistJkYvNiRGNEYnRjFGK0YrKiYiIiVGKy0mRi82JEYnRidGMUYrISIiRitJImhHRiVGPUYr">LCQqJiwoLSZJInVHNiI2JCIiIiIiIzYjSSJ0R0YoRiotJkYnNiQiIiRGK0YsRjEtJkYnNiRGK0YrRiwhIiVGKkkiaEdGKCEiIiNGKkYr</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJWR5ZHhHNiI2IyIiIywkKigjIiIiRidGK0kiaEdGJSEiIiwmLSZJInVHRiU2JCwmSSJtR0YlRitGK0YrRic2I0kidEdGJUYrLSZGMTYkLCZGNEYrRitGLUYnRjVGLUYrRis=">LCQqJkkiaEc2IiEiIiwmLSZJInVHRiU2JCwmSSJtR0YlIiIiRi5GLiIiIzYjSSJ0R0YlRi4tJkYqNiQsJkYtRi5GJkYuRi9GMEYmRi4jRi5GLw==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJ2QyeWR4Mkc2IjYjIiIjKiYpSSJoR0YlRichIiIsKC0mSSJ1R0YlNiQsJkkibUdGJSIiIkYzRitGJzYjSSJ0R0YlRjMqJkYnRjMtJkYvNiRGMkYnRjRGM0YrLSZGLzYkLCZGMkYzRjNGM0YnRjRGM0Yz">KiZJImhHNiIhIiMsKC0mSSJ1R0YkNiQsJkkibUdGJCIiIiEiIkYtIiIjNiNJInRHRiRGLS0mRik2JEYsRi9GMEYlLSZGKTYkLCZGLEYtRi1GLUYvRjBGLUYt</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="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to NN do bc1[i]:=subs(diff(u[1](x,t),x)=dydxf[1],diff(u[2](x,t),x)=dydxf[2],u[1](x,t)=u[0,1](t),u[2](x,t)=u[0,2](t),x=0,bc1[i]);od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJGJjMUc2IjYjIiIiLCYtJkkidUdGJTYkIiIhRic2I0kidEdGJUYnRichIiI=">LCYtJkkidUc2IjYkIiIhIiIiNiNJInRHRiZGKSEiIkYp</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJGJjMUc2IjYjIiIjLCYtJkkidUdGJTYkIiIhRic2I0kidEdGJSIiIkYwISIi">LCYtJkkidUc2IjYkIiIhIiIjNiNJInRHRiYiIiIhIiJGLA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to NN do bc2[i]:=subs(diff(u[1](x,t),x)=dydxb[1],diff(u[2](x,t),x)=dydxb[2],u[1](x,t)=u[N+1,1](t),u[2](x,t)=u[N+1,2](t),x=L,bc2[i]);od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJGJjMkc2IjYjIiIiLCgqJiIiJEYnLSZJInVHRiU2JEYqRic2I0kidEdGJUYnRicqKCNGJyIiI0YnLCgtJkYtNiRGJ0YnRi9GJ0YpRicqJiIiJUYnLSZGLTYkRjNGJ0YvRichIiJGJ0kiaEdGJUY9RidGKkY9">LCgtJkkidUc2IjYkIiIkIiIiNiNJInRHRiZGKComLCgtJkYlNiRGKUYpRipGKUYjRigtJkYlNiQiIiNGKUYqISIlRilJImhHRiYhIiIjRilGNCEiJEYp</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJGJjMkc2IjYjIiIjLCgqKCMiIiZGJyIiIiwoLSZJInVHRiU2JEYsRic2I0kidEdGJUYsKiYiIiRGLC0mRjA2JEY1RidGMkYsRiwqJiIiJUYsLSZGMDYkRidGJ0YyRiwhIiJGLEkiaEdGJUY+RiwqJiQiKy5dIilmYSEiKUYsLSZGMDYkRjVGLEYyRixGPkZBRiw=">LCgqJiwoLSZJInVHNiI2JCIiIiIiIzYjSSJ0R0YoRiotJkYnNiQiIiRGK0YsRjEtJkYnNiRGK0YrRiwhIiVGKkkiaEdGKCEiIiMiIiZGKy0mRic2JEYxRipGLCQhKy5dIilmYSEiKSQiKy5dIilmYUY/Rio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to NN do eq[0,i]:=bc1[i];eq[N+1,i]:=bc2[i];od; </Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiQiIiEiIiIsJi0mSSJ1R0YlRiY2I0kidEdGJUYoRighIiI=">LCYtJkkidUc2IjYkIiIhIiIiNiNJInRHRiZGKSEiIkYp</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiQiIiQiIiIsKComRidGKC0mSSJ1R0YlRiY2I0kidEdGJUYoRigqKCNGKCIiI0YoLCgtJkYtNiRGKEYoRi5GKEYqRigqJiIiJUYoLSZGLTYkRjJGKEYuRighIiJGKEkiaEdGJUY8RihGJ0Y8">LCgtJkkidUc2IjYkIiIkIiIiNiNJInRHRiZGKComLCgtJkYlNiRGKUYpRipGKUYjRigtJkYlNiQiIiNGKUYqISIlRilJImhHRiYhIiIjRilGNCEiJEYp</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiQiIiEiIiMsJi0mSSJ1R0YlRiY2I0kidEdGJSIiIkYvISIi">LCYtJkkidUc2IjYkIiIhIiIjNiNJInRHRiYiIiIhIiJGLA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiQiIiQiIiMsKCooIyIiJkYoIiIiLCgtJkkidUdGJTYkRi1GKDYjSSJ0R0YlRi0qJkYnRi0tJkYxRiZGM0YtRi0qJiIiJUYtLSZGMTYkRihGKEYzRi0hIiJGLUkiaEdGJUY9Ri0qJiQiKy5dIilmYSEiKUYtLSZGMTYkRidGLUYzRi1GPUZARi0=">LCgqJiwoLSZJInVHNiI2JCIiIiIiIzYjSSJ0R0YoRiotJkYnNiQiIiRGK0YsRjEtJkYnNiRGK0YrRiwhIiVGKkkiaEdGKCEiIiMiIiZGKy0mRic2JEYxRipGLCQhKy5dIilmYSEiKSQiKy5dIilmYUY/Rio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L64" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Convert the first governing equation 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,1]:=diff(u[i,1](t),t)= subs(diff(u[1](x,t),x$2) = subs(m=i,d2ydx2[1]),diff(u[2](x,t),x$2) = subs(m=i,d2ydx2[2]),diff(u[1](x,t),x) = subs(m=i,dydx[1]),diff(u[2](x,t),x) = subs(m=i,dydx[2]),u[1](x,t)=u[i,1](t),u[2](x,t)=u[i,2](t),x=i*h,rhs(ge[1]));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiQiIiJGJy8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJInVHRiVGJjYjSSJ0R0YlRjEsKioqI0YnIiIlRicpSSJoR0YlIiIjISIiLCYtJkYvNiRGOEY4RjBGJy0mRi82JCIiIUY4RjBGOUYnLCYtJkYvNiRGOEYnRjBGJy0mRi82JEZBRidGMEY5RidGJyooLCYtJkYvNiRGJ0Y4RjBGJ0YnRjlGJ0Y2RjksKEZGRicqJkY4RidGLUYnRjlGQ0YnRidGJyomLCoqKCIjO0YnRjdGJ0YxRidGJyomRjhGJ0YxRidGOSomRlNGJ0ZLRidGOUZTRidGJywmRi1GJ0YnRjlGJ0YnKigiIzVGJ0Y3RictSSRleHBHNiRGK0koX3N5c2xpYkdGJTYjLCQqJkY1RidGN0YnRjlGJ0Yn">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYkIiIiRiw2I0kidEdGKkYuLCoqKEkiaEdGKiEiIywmLSZGKTYkIiIjRjdGLUYsLSZGKTYkIiIhRjdGLSEiIkYsLCYtJkYpNiRGN0YsRi1GLC0mRik2JEY7RixGLUY8RiwjRiwiIiUqKCwmLSZGKTYkRixGN0YtRixGPEYsRixGMUYyLChGQUYsRidGMkY+RixGLEYsKiYsKiomRjFGLEYuRiwiIztGLkYyRkghIztGT0YsRiwsJkYnRixGPEYsRixGLComRjFGLC1JJGV4cEc2JEYlSShfc3lzbGliR0YqNiMsJEYxISIlRiwiIzU=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiQiIiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYyLCoqKiNGKCIiJUYoKUkiaEdGJUYnISIiLCYtJkYwNiQiIiRGJ0YxRigtJkYwNiRGKEYnRjFGOUYoLCYtJkYwNiRGPkYoRjFGKC0mRjA2JEYoRihGMUY5RihGKCooLCYtJkYwNiRGJ0YnRjFGKEYoRjlGKEY3RjksKEZGRigqJkYnRihGLkYoRjlGQ0YoRihGKComLCoqKCIjS0YoRjhGKEYyRihGKComRidGKEYyRihGOSomIiM7RihGS0YoRjlGVkYoRigsJkYuRihGKEY5RihGKCooIiM/RihGOEYoLUkkZXhwRzYkRixJKF9zeXNsaWJHRiU2IywkKiYiIilGKEY4RihGOUYoRig=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYkIiIjIiIiNiNJInRHRipGLywqKihJImhHRiohIiMsJi0mRik2JCIiJEYsRi5GLS0mRik2JEYtRixGLiEiIkYtLCYtJkYpNiRGOEYtRi5GLS0mRik2JEYtRi1GLkY8Ri0jRi0iIiUqKCwmLSZGKTYkRixGLEYuRi1GPEYtRi1GMkYzLChGQUYtRidGM0Y+Ri1GLUYtKiYsKiomRjJGLUYvRi0iI0tGL0YzRkghIzsiIztGLUYtLCZGJ0YtRjxGLUYtRi0qJkYyRi0tSSRleHBHNiRGJUkoX3N5c2xpYkdGKjYjLCRGMiEiKUYtIiM/</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L65" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Convert the second governing equation to the finite difference form:</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N do eq[i,2]:=diff(u[i,2](t),t)= subs(diff(u[1](x,t),x$2) = subs(m=i,d2ydx2[1]),diff(u[2](x,t),x$2) = subs(m=i,d2ydx2[2]),diff(u[1](x,t),x) = subs(m=i,dydx[1]),diff(u[2](x,t),x) = subs(m=i,dydx[2]),u[1](x,t)=u[i,1](t),u[2](x,t)=u[i,2](t),x=i*h,rhs(ge[2]));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiQiIiIiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYyLDAqJilJImhHRiVGKCEiIiwoLSZGMDYkIiIhRihGMUYnKiZGKEYnRi5GJ0Y3LSZGMDYkRihGKEYxRidGJ0YnKigjRidGKEYnRjZGNywmLSZGMDYkRihGJ0YxRictJkYwNiRGPEYnRjFGN0YnRicqJiIiJUYnLSZGMDYkRidGJ0YxRidGJ0ZLRjcqJEY1RidGJyomRihGJ0YyRidGNyooIiM1RidGMkYnLUkkZXhwRzYkRixJKF9zeXNsaWJHRiU2IywkKiZGS0YnRjZGJ0Y3RidGNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYkIiIiIiIjNiNJInRHRipGLywwKiZJImhHRiohIiMsKC0mRik2JCIiIUYtRi5GLEYnRjMtJkYpNiRGLUYtRi5GLEYsRiwqJkYyISIiLCYtJkYpNiRGLUYsRi5GLC0mRik2JEY4RixGLkY9RiwjRixGLS0mRik2JEYsRixGLiIiJSEiJUYsKiRGMkYtRixGL0YzKiZGL0YsLUkkZXhwRzYkRiVJKF9zeXNsaWJHRio2IywkRjJGSkYsISM1</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiQiIiNGJy8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJInVHRiVGJjYjSSJ0R0YlRjEsMComKUkiaEdGJUYnISIiLCgtJkYvNiQiIiJGJ0YwRjsqJkYnRjtGLUY7RjYtJkYvNiQiIiRGJ0YwRjtGO0Y7KigjRjtGJ0Y7RjVGNiwmLSZGLzYkRkBGO0YwRjstJkYvNiRGO0Y7RjBGNkY7RjsqJiIiJUY7LSZGLzYkRidGO0YwRjtGO0ZLRjYqJkZLRjtGNEY7RjsqJkYnRjtGMUY7RjYqKCIjNUY7RjFGOy1JJGV4cEc2JEYrSShfc3lzbGliR0YlNiMsJComIiIpRjtGNUY7RjZGO0Y2">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYkIiIjRiw2I0kidEdGKkYuLDAqJkkiaEdGKiEiIywoLSZGKTYkIiIiRixGLUY3RidGMi0mRik2JCIiJEYsRi1GN0Y3RjcqJkYxISIiLCYtJkYpNiRGO0Y3Ri1GNy0mRik2JEY3RjdGLUY9RjcjRjdGLC0mRik2JEYsRjdGLSIiJSEiJUY3KiRGMUYsRklGLkYyKiZGLkY3LUkkZXhwRzYkRiVJKF9zeXNsaWJHRio2IywkRjEhIilGNyEjNQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to NN do u[0,i](t):=(solve(eq[0,i],u[0,i](t)));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiQiIiEiIiI2I0kidEdGJkYp">IiIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiQiIiEiIiM2I0kidEdGJiIiIg==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L66" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Eliminate the boundary values:</Text-field>
</Input>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to NN do u[N+1,i](t):=(solve(eq[N+1,i],u[N+1,i](t)));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiQiIiQiIiI2I0kidEdGJiwkKigjRilGKEYpLCgtJkYlNiRGKUYpRiohIiIqJiIiJUYpLSZGJTYkIiIjRilGKkYpRikqJiIiJ0YpSSJoR0YmRilGKUYpLCYqJkY5RilGPEYpRilGKUYpRjNGKQ==">LCQqJiwoLSZJInVHNiI2JCIiIkYqNiNJInRHRighIiItJkYnNiQiIiNGKkYrIiIlSSJoR0YoIiInRiosJkYzRjFGKkYqRi0jRioiIiQ=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiQiIiQiIiM2I0kidEdGJiwkKigkIitMTExMOCEjPSIiIiwyKigkIiorKysrJiIiIUYxLSZGJTYkRjFGKUYqRjFJImhHRiZGMUYxKiYkIiorKytdI0Y2RjFGN0YxRjEqKCQiKysrKys/RjZGMS0mRiU2JEYpRilGKkYxRjpGMSEiIiomJCIrKysrKzVGNkYxRkFGMUZEKigkIitNJFEqPj1GNkYxRjpGMS0mRiU2JEYxRjFGKkYxRjEqKCQiK09MdnpzRjZGMUY6RjEtJkYlNiRGKUYxRipGMUZEKiYkRilGNkYxKUY6RilGMUYxKiYkIisuXSIpZmFGNkYxRjpGMUYxRjEsJiomRlVGMUY6RjFGMSRGMUY2RjFGREZE">LCQqJiwyKiYtJkkidUc2IjYkIiIiIiIjNiNJInRHRilGK0kiaEdGKUYrJCIqKysrKyYiIiFGJiQiKisrK10jRjIqJi0mRig2JEYsRixGLUYrRi9GKyQhKysrKys/RjJGNiQhKysrKys1RjIqJkYvRistJkYoNiRGK0YrRi1GKyQiK00kUSo+PUYyKiZGL0YrLSZGKDYkRixGK0YtRiskIStPTHZ6c0YyKiRGL0YsJEYsRjJGLyQiKy5dIilmYUYyRissJkYvRkokRitGMkYrISIiJCErTExMTDghIz0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">h:=L/(N+1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiaEc2IiMiIiIiIiQ=">IyIiIiIiJA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N do eq[i,1]:=eval(eq[i,1]);od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiQiIiJGJy8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJInVHRiVGJjYjSSJ0R0YlRjEsKiooIyIiKiIiJUYnLCYtJkYvNiQiIiNGO0YwRidGJyEiIkYnLCYtJkYvNiRGO0YnRjBGJ0YnRjxGJ0YnKihGNUYnLCYtJkYvNiRGJ0Y7RjBGJ0YnRjxGJywoRidGJyomRjtGJ0YtRidGPEY+RidGJ0YnKiYsKComIyIjNSIiJEYnRjFGJ0YnKiYiIztGJ0ZDRidGPEZPRidGJywmRi1GJ0YnRjxGJ0YnKiZGS0YnLUkkZXhwRzYkRitJKF9zeXNsaWJHRiU2IyMhIiVGTUYnRic=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYkIiIiRiw2I0kidEdGKkYuLCoqJiwmLSZGKTYkIiIjRjVGLUYsISIiRixGLCwmLSZGKTYkRjVGLEYtRixGNkYsRiwjIiIqIiIlKiYsJi0mRik2JEYsRjVGLUYsRjZGLEYsLChGLEYsRichIiNGOEYsRixGPComLChGLiMiIzUiIiRGQCEjOyIjO0YsRiwsJkYnRixGNkYsRixGLC1JJGV4cEc2JEYlSShfc3lzbGliR0YqNiMjISIlRklGRw==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYkIiIjIiIiNiNJInRHRipGLywqKiYsLC0mRik2JEYtRixGLiQhK0xMTEw4ISIqLSZGKTYkRixGLEYuJCIrTExMTDhGOC0mRik2JEYtRi1GLiQhKykpKW9KJlshIzVGJyQiK2N2RVQ+RjgkISttMSZmWCJGOEYtRi0sKEY+IyEiJyIiJkYnIyIiJUZLI0YsRktGLUYtIyIiKkZNKiYsJkY5Ri0hIiJGLUYtLChGPkZMRidGSUZORi1GLUZQKiYsKEYvIyIjRSIiJEY5ISM7IiM7Ri1GLSwmRidGLUZTRi1GLUYtLUkkZXhwRzYkRiVJKF9zeXNsaWJHRio2IyMhIilGWSMiIz9GWQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N do eq[i,2]:=eval(eq[i,2]);od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiQiIiIiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYyLDAjIiNsIiM9RicqJkY2RidGLkYnISIiKiYiIipGJy0mRjA2JEYoRihGMUYnRicqJiMiIiRGKEYnLSZGMDYkRihGJ0YxRidGJyomIiIlRictJkYwNiRGJ0YnRjFGJ0YnKiZGKEYnRjJGJ0Y4KigiIzVGJ0YyRictSSRleHBHNiRGLEkoX3N5c2xpYkdGJTYjIyEiJUZARidGOA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYkIiIiIiIjNiNJInRHRipGLywwIyIjbCIjPUYsRichIz0tJkYpNiRGLUYtRi4iIiotJkYpNiRGLUYsRi4jIiIkRi0tJkYpNiRGLEYsRi4iIiVGLyEiIyomRi9GLC1JJGV4cEc2JEYlSShfc3lzbGliR0YqNiMjISIlRj1GLCEjNQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiQiIiNGJy8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLSZJInVHRiVGJjYjSSJ0R0YlRjEsMComJCIrKysrK2chIioiIiItJkYvNiRGN0YnRjBGN0Y3KiYkIiorKysrJyEiKUY3Ri1GNyEiIiomJCIrKz8meTsnRjZGNy0mRi82JEY3RjdGMEY3Rj8qJiQiKyszOW5BRj5GNy0mRi82JEYnRjdGMEY3RjckIitjNiJmZyJGPkY/KiZGJ0Y3RjFGN0Y/KigiIzVGN0YxRjctSSRleHBHNiRGK0koX3N5c2xpYkdGJTYjI0Y+IiIkRjdGPw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYkIiIjRiw2I0kidEdGKkYuLDAtJkYpNiQiIiJGLEYtJCIrKysrK2chIipGJyQhKisrKysnISIpLSZGKTYkRjNGM0YtJCErKz8meTsnRjYtJkYpNiRGLEYzRi0kIisrMzluQUY5JCErYzYiZmciRjlGM0YuISIjKiZGLkYzLUkkZXhwRzYkRiVJKF9zeXNsaWJHRio2IyNGOSIiJEYzISM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L67" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Store the governing equations in eqs:</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=seq(seq((eq[i,j]),i=1..N),j=1..NN);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFzRzYiNiYvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YkNiQiIiJGLzYjSSJ0R0YkRjEsKiooIyIiKiIiJUYvLCYtJkYtNiQiIiNGO0YwRi9GLyEiIkYvLCYtJkYtNiRGO0YvRjBGL0YvRjxGL0YvKihGNUYvLCYtJkYtNiRGL0Y7RjBGL0YvRjxGLywoRi9GLyomRjtGL0YrRi9GPEY+Ri9GL0YvKiYsKComIyIjNSIiJEYvRjFGL0YvKiYiIztGL0ZDRi9GPEZPRi9GLywmRitGL0YvRjxGL0YvKiZGS0YvLUkkZXhwRzYkRilJKF9zeXNsaWJHRiQ2IyMhIiVGTUYvRi8vLUYoNiRGPkYxLCoqKEY0Ri8sLComJCIrTExMTDghIipGL0ZDRi9GPComRmpuRi9GOEYvRi8qJiQiKykpKW9KJlshIzVGL0YrRi9GPComJCIrY3ZFVD5GXG9GL0Y+Ri9GLyQiK20xJmZYIkZcb0Y8Ri8sKComIyIiJyIiJkYvRitGL0Y8KiYjRjZGW3BGL0Y+Ri9GLyNGO0ZbcEYvRi9GLyooRjVGL0Y3Ri8sKComRl1wRi9GK0YvRi8qJkZpb0YvRj5GL0Y8Rl5wRi9GL0YvKiYsKComIyIjRUZNRi9GMUYvRi8qJkZPRi9GOEYvRjxGT0YvRi9GPUYvRi8qJiMiIz9GTUYvLUZTNiMjISIpRk1GL0YvLy1GKDYkRkNGMSwwIyIjbCIjPUYvKiZGZnFGL0ZDRi9GPComRjVGL0Y4Ri9GLyomI0ZNRjtGL0Y+Ri9GLyomRjZGL0YrRi9GLyomRjtGL0YxRi9GPCooRkxGL0YxRi9GUkYvRjwvLUYoNiRGOEYxLDAqJiQiKysrKytnRlxvRi9GQ0YvRi8qJiQiKisrKysnRl9xRi9GOEYvRjwqJiQiKys/Jnk7J0Zcb0YvRitGL0Y8KiYkIisrMzluQUZfcUYvRj5GL0YvJCIrYzYiZmciRl9xRjxGXHJGPCooRkxGL0YxRi9GXHFGL0Y8">NiYvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1RzYiNiQiIiJGLTYjSSJ0R0YrRi8sKiomLCYtJkYqNiQiIiNGNkYuRi0hIiJGLUYtLCYtJkYqNiRGNkYtRi5GLUY3Ri1GLSMiIioiIiUqJiwmLSZGKjYkRi1GNkYuRi1GN0YtRi0sKEYtRi1GKCEiI0Y5Ri1GLUY9KiYsKEYvIyIjNSIiJEZBISM7IiM7Ri1GLSwmRihGLUY3Ri1GLUYtLUkkZXhwRzYkRiZJKF9zeXNsaWJHRis2IyMhIiVGSkZILy1GJTYkRjlGLywqKiYsLEZBJCErTExMTDghIipGMyQiK0xMTEw4RmduRigkISspKSlvSiZbISM1RjkkIitjdkVUPkZnbiQhK20xJmZYIkZnbkYtRi0sKEYoIyEiJyIiJkY5I0Y+RmRvI0Y2RmRvRi1GLUY8KiZGMkYtLChGKEZlb0Y5RmJvRmZvRi1GLUY9KiYsKEYvIyIjRUZKRjNGS0ZMRi1GLUY4Ri1GLS1GTzYjIyEiKUZKIyIjP0ZKLy1GJTYkRkFGLywwIyIjbCIjPUYtRkEhIz1GM0Y9RjkjRkpGNkYoRj5GL0ZFKiZGL0YtRk5GLUZcby8tRiU2JEYzRi8sMEZBJCIrKysrK2dGZ25GMyQhKisrKysnRmBwRigkISsrPyZ5OydGZ25GOSQiKyszOW5BRmBwJCErYzYiZmciRmBwRi1GL0ZFKiZGL0YtRl1wRi1GXG8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L68" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Store the dependent variables in Y:</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=seq(seq(u[i,j](t),i=1..N),j=1..NN);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiWUc2IjYmLSZJInVHRiQ2JCIiIkYqNiNJInRHRiQtJkYoNiQiIiNGKkYrLSZGKDYkRipGMEYrLSZGKDYkRjBGMEYr">NiYtJkkidUc2IjYkIiIiRig2I0kidEdGJi0mRiU2JCIiI0YoRiktJkYlNiRGKEYuRiktJkYlNiRGLkYuRik=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L69" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Store the initial conditions in ICs:</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ICs:=seq(u[i,1](0)=rhs(IC[1]),i=1..N),seq(u[i,2](0)=rhs(IC[2]),i=1..N);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkSUNzRzYiNiYvLSZJInVHRiQ2JCIiIkYrNiMiIiFGKy8tJkYpNiQiIiNGK0YsRisvLSZGKTYkRitGMkYsRisvLSZGKTYkRjJGMkYsRis=">NiYvLSZJInVHNiI2JCIiIkYpNiMiIiFGKS8tJkYmNiQiIiNGKUYqRikvLSZGJjYkRilGMEYqRikvLSZGJjYkRjBGMEYqRik=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqs,ICs},{Y},type=numeric,stiff=true,maxfun=1000000,abserr=1e-6,relerr=1e-5,output=listprocedure);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NycvSSJ0RzYiZio2I0YkNidJJHJlc0dGJUklZGF0YUdGJUkpc29sbnByb2NHRiVJKW91dHBvaW50R0YlRiQ2I0lpbkNvcHlyaWdodH4oYyl+MjAwMH5ieX5XYXRlcmxvb35NYXBsZX5JbmMufkFsbH5yaWdodHN+cmVzZXJ2ZWQuR0YlRiVDKT5JOF9FbnZEU051bWVyaWNTYXZlRGlnaXRzR0YlSSdEaWdpdHNHRiU+RjIiIzlAJS9JLV9FbnZJbkZzb2x2ZUdGJUkldHJ1ZUclKnByb3RlY3RlZEc+OCctJkkmZXZhbGZHRjk2I0YxNiM5JD5GOy1GPkZAPjglLUklZXZhbEdGOTYjJkk8ZHNvbHZlL251bWVyaWMvZGF0YS9tb2R1bGVzR0koX3N5c2xpYkdGJTYjIiIiPjgmLV9GRUkkR2V0R0YlNiNRL3NvbG5fcHJvY2VkdXJlRiVAJDQtSSV0eXBlR0Y5NiRGOy5JKG51bWVyaWNHRjlDJEAuLUknbWVtYmVyR0Y5NiRGQTcrUSZzdGFydEYlLkkmc3RhcnRHRiVRJ21ldGhvZEYlLkknbWV0aG9kR0YlUSVsZWZ0RiVRJnJpZ2h0RiVRKWxlZnRkYXRhRiVRKnJpZ2h0ZGF0YUYlUStlbmdpbmVkYXRhRiVDJEAlLUZpbjYkRkE3JEZdb0Zgbz44JC1GTzYjLUkoY29udmVydEdGOTYkRkEuSSdzdHJpbmdHRjk+Rl1wLUZPRkBAJi1GWDYkRl1wLkkmYXJyYXlHRjlPLUZHNiRGXXBGTTBGXXBRKXByb2NuYW1lRiVPRl1wLUZpbjYkRkE3JFElbGFzdEYlUShpbml0aWFsRiVDJEZlcEAkLUZYNiRGXXAuSSVsaXN0R0Y5TyZGXXBGTC1GaW42JEZBNyQuSSVsYXN0R0YlLkkoaW5pdGlhbEdGJUMkRlxwRmhxMy1GWDYkRjtJIj1HRjktRmluNiQtSSRsaHNHRjk2I0Y7NyRGZnFGZHJDJEAlLUZYNiQtSSRyaHNHRjlGX3NGW3I+Rl1wLUZPNiMvRmZxNyQiIiEtSSNvcEdGOTYjRmVzPkZdcC1GTzYjL0ZmcTckRk1GZXNGaHEvRjtRLnNvbG5wcm9jZWR1cmVGJU8tRkc2I0ZPL0Y7UShzeXN2YXJzRiVPLUZRNiNGW3VAJTA5IUkodW5rbm93bkdGJU8tLkZhdUZAQyQ+OCgtSShwb2ludHRvR0Y5NiMmLUZRNiNRMHNvbG5fcHJvY2VkdXJlc0YlRkxPLS5GaHVGQFolQyQ+Rl1wLUZPRl9zRl5yRiVZRiVGJUYlRiUvLSZJInVHRiU2JEZNRk1GJ2YqRic2J0YpRipGK0YsSSp1WzEsMV0odClHRiVGLUYlQylGMEYzRjVGREZOQCRGVkMkQC5GaG5GZ29GYnFDJEZlcEAkRmlxTyZGXXA2IyIiI0ZfckMkRlxwRmV3RmdyQyRAJUZjc0Zncz5GXXAtRk82Iy9GZnE3JEZpd0Zlc0Zld0ZldEZndEZqdEZcdUAlRmB1RmN1QyQ+Rmh1LUZqdTYjJkZddkZod0ZgdlolQyRGZXZGZ3dGJUZndkYlRiVGJS8tJkZbdzYkRk1GaXdGJ2YqRic2J0YpRipGK0YsSSp1WzEsMl0odClHRiVGLUYlQylGMEYzRjVGREZOQCRGVkMkQC5GaG5GZ29GYnFDJEZlcEAkRmlxTyZGXXA2IyIiJEZfckMkRlxwRmZ5RmdyQyRAJUZjc0Zncz5GXXAtRk82Iy9GZnE3JEZqeUZlc0ZmeUZldEZndEZqdEZcdUAlRmB1RmN1QyQ+Rmh1LUZqdTYjJkZddkZpeUZgdlolQyRGZXZGaHlGJUZndkYlRiVGJS8tJkZbdzYkRml3Rk1GJ2YqRic2J0YpRipGK0YsSSp1WzIsMV0odClHRiVGLUYlQylGMEYzRjVGREZOQCRGVkMkQC5GaG5GZ29GYnFDJEZlcEAkRmlxTyZGXXA2IyIiJUZfckMkRlxwRmdbbEZnckMkQCVGY3NGZ3M+Rl1wLUZPNiMvRmZxNyRGW1xsRmVzRmdbbEZldEZndEZqdEZcdUAlRmB1RmN1QyQ+Rmh1LUZqdTYjJkZddkZqW2xGYHZaJUMkRmV2RmlbbEYlRmd2RiVGJUYlLy0mRlt3NiRGaXdGaXdGJ2YqRic2J0YpRipGK0YsSSp1WzIsMl0odClHRiVGLUYlQylGMEYzRjVGREZOQCRGVkMkQC5GaG5GZ29GYnFDJEZlcEAkRmlxTyZGXXA2IyIiJkZfckMkRlxwRmhdbEZnckMkQCVGY3NGZ3M+Rl1wLUZPNiMvRmZxNyRGXF5sRmVzRmhdbEZldEZndEZqdEZcdUAlRmB1RmN1QyQ+Rmh1LUZqdTYjJkZddkZbXmxGYHZaJUMkRmV2RmpdbEYlRmd2RiVGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for j to NN do for i to N do U[i,j]:=subs(sol,u[i,j](t));od:od;</Text-field>
</Input>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to NN do U[0,i]:=subs(u[1,1](t)=U[1,1],u[1,2](t)=U[1,2],u[2,1](t)=U[2,1],u[2,2](t)=U[2,2],u[0,i](t));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIlVHNiI2JCIiISIiIkYo">IiIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIlVHNiI2JCIiISIiIyIiIg==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to NN do U[N+1,i]:=eval(subs(u[N,1](t)=U[N,1],u[N,2](t)=U[N,2],u[N-1,1](t)=U[N-1,1],u[N-1,2](t)=U[N-1,2],u[N+1,i](t)));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIlVHNiI2JCIiJCIiIiwoKiYjRigiIiZGKCZGJDYkRihGKEYoISIiKiYjIiIlRixGKCZGJDYkIiIjRihGKEYoI0Y1RixGKA==">LCgmSSJVRzYiNiQiIiJGJyMhIiIiIiYmRiQ2JCIiI0YnIyIiJUYqI0YtRipGJw==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIlVHNiI2JCIiJCIiIywsKiYkIitLTExMTCEjNSIiIiZGJDYkRi5GKEYuISIiKiYkIitMTExMOCEiKkYuJkYkNiRGKEYoRi5GLiomJCIrKSkpb0omW0YtRi4mRiQ2JEYuRi5GLkYxKiYkIitjdkVUPkY1Ri4mRiQ2JEYoRi5GLkYuJCIrbTEmZlgiRjVGMQ==">LCwmSSJVRzYiNiQiIiIiIiMkIStLTExMTCEjNSZGJDYkRihGKCQiK0xMTEw4ISIqJkYkNiRGJ0YnJCErKSkpb0omW0YrJkYkNiRGKEYnJCIrY3ZFVD5GMCQhK20xJmZYIkYwRic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L70" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The numerical solution obtained is compared with the exact analytical solution at x = 1:</Text-field>
</Input>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ua:=1+10*x*t*exp(-4*x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdWFHNiIsJiIiIkYmKioiIzVGJkkieEdGJEYmSSJ0R0YkRiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiYiIiVGJkYpRiYhIiJGJkYm">LCYiIiJGIyooSSJ4RzYiRiNJInRHRiZGIy1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjLCRGJSEiJUYjIiM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">va:=1+x^2*t;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdmFHNiIsJiIiIkYmKiYpSSJ4R0YkIiIjRiZJInRHRiRGJkYm">LCYiIiJGIyomSSJ4RzYiIiIjSSJ0R0YmRiNGIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U[N+1,1](1);evalf(subs(x=1.,t=1.,ua));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIrXCMpW3A2ISIq</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIrKlFjSj0iISIq</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalf(U[N+1,2](1));evalf(subs(x=1.,t=1.,va));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIrKT4qM2g+ISIq</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIiIyIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U[N+1,1](2);evalf(subs(x=1.,t=2.,ua));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIrb01kVDghIio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIreUZKbTghIio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalf(U[N+1,2](2));evalf(subs(x=1.,t=2.,va));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIrKkcjKjMjSCEiKg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIiJCIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L71" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We obtain reasonable results even with N=2 node points.</Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tf:=1.;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdGZHNiIkIiIiIiIh">JCIiIiIiIQ==</Equation></Text-field>
</Output>
</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="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="PkkjVDFHNiI3QSQiIiFGJyQiK0xMTExMISM2JCIrbm1tbW1GKiQiKysrKys1ISM1JCIrTExMTDhGLyQiK25tbW07Ri8kIisrKysrP0YvJCIrTExMTEJGLyQiK25tbW1FRi8kIisrKysrSUYvJEYpRi8kIitubW1tT0YvJCIrKysrK1NGLyQiK0xMTExWRi8kIitubW1tWUYvJCIrKysrK11GLyQiK0xMTExgRi8kIitubW1tY0YvJCIrKysrK2dGLyQiK0xMTExqRi8kRixGLyQiKysrKytxRi8kIitMTExMdEYvJCIrbm1tbXdGLyQiKysrKyshKUYvJCIrTExMTCQpRi8kIitubW1tJylGLyQiKysrKyshKkYvJCIrTExMTCQqRi8kIitubW1tJypGLyRGLiEiKg==">N0EkIiIhRiQkIitMTExMTCEjNiQiK25tbW1tRickIisrKysrNSEjNSQiK0xMTEw4RiwkIitubW1tO0YsJCIrKysrKz9GLCQiK0xMTExCRiwkIitubW1tRUYsJCIrKysrK0lGLCRGJkYsJCIrbm1tbU9GLCQiKysrKytTRiwkIitMTExMVkYsJCIrbm1tbVlGLCQiKysrKytdRiwkIitMTExMYEYsJCIrbm1tbWNGLCQiKysrKytnRiwkIitMTExMakYsJEYpRiwkIisrKysrcUYsJCIrTExMTHRGLCQiK25tbW13RiwkIisrKysrISlGLCQiK0xMTEwkKUYsJCIrbm1tbScpRiwkIisrKysrISpGLCQiK0xMTEwkKkYsJCIrbm1tbScqRiwkRishIio=</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="PkkjUFBHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIiU7RioiI0o3Ig==">PTYiNiQ7IiIiIiIlO0YmIiNKRVxbbCE=</Equation></Text-field>
</Output>
</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[1])));od:</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-1,1](t)));od;od:</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. 5.2.11.&quot;,labels=[x,t,&quot;u&quot;],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, 5708 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(ua,x=0..1,t=0..1,axes=boxed,title=&quot;Figure Exp. 5.2.12.&quot;,labels=[x,t,&quot;ua&quot;],orientation=[-45,60]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="three-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0">[encoded data, 13696 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L48" 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="PkkjUFBHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIiU7RioiI0o3Ig==">PTYiNiQ7IiIiIiIlO0YmIiNKRVxbbCE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L49" 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[2])));od:</Text-field>
</Input>
</Group>
<Group labelreference="L50" 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-1,2](t)));od;od:</Text-field>
</Input>
</Group>
<Group labelreference="L51" 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="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">surfdata(plotdata,axes=boxed,title=&quot;Figure Exp. 5.2.13.&quot;,labels=[x,t,&quot;v&quot;],orientation=[-45,60]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="three-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0">[encoded data, 5708 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(va,x=0..1,t=0..1,labels=[x,t,&quot;va&quot;],axes=boxed,title=&quot;Figure Exp. 5.2.14.&quot;,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, 13696 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L72" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The results obtained with N = 10 are:</Text-field>
</Input>
</Group>
</Worksheet>