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<Task-table>
    <Task-category name="&lt;default&gt;">
    </Task-category>
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<Annotation-table>
    <Annotation-category name="&lt;default&gt;">
    </Annotation-category>
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<Task>
</Task>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 3.7b </Font></Text-field>
</Input>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
</Group>
<Group labelreference="L3" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(linalg):with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">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="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">L:=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTEc2IiIiIg==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=diff(y(x),x$2)-Pe*diff(y(x),x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIsJi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ5R0YkNiNJInhHRiQtSSIkR0YoNiRGLSIiIyIiIiomSSNQZUdGJEYyLUYnNiRGKkYtRjIhIiI=">LCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYkNiQtSSJ5RzYiNiNJInhHRitGLUYtIiIiKiZJI1BlR0YrRi5GJ0YuISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=y(x)=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLy1JInlHRiQ2I0kieEdGJCIiIg==">Ly1JInlHNiI2I0kieEdGJSIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=y(x)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLy1JInlHRiQ2I0kieEdGJCIiIQ==">Ly1JInlHNiI2I0kieEdGJSIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The central difference expression for the second and first derivatives are</Text-field>
</Input>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">d2ydx2:=(y[m+1]-2*y[m]+y[m-1])/h^2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknZDJ5ZHgyRzYiKiYsKCZJInlHRiQ2IywmSSJtR0YkIiIiRixGLEYsKiYiIiNGLCZGKDYjRitGLCEiIiZGKDYjLCZGK0YsRixGMUYsRiwpSSJoR0YkRi5GMQ==">KiYsKCZJInlHNiI2IywmSSJtR0YmIiIiRipGKkYqJkYlNiNGKSEiIyZGJTYjLCZGKUYqISIiRipGKkYqSSJoR0YmRi0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydx:=(y[m]-y[m-1])/h;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklZHlkeEc2IiomLCYmSSJ5R0YkNiNJIm1HRiQiIiImRig2IywmRipGK0YrISIiRi9GK0kiaEdGJEYv">KiYsJiZJInlHNiI2I0kibUdGJiIiIiZGJTYjLCZGKEYpISIiRilGLUYpSSJoR0YmRi0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> The governing equation in finite difference form is:</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq[m]:=subs(diff(y(x),x$2)=d2ydx2,diff(y(x),x)=dydx,y(x)=y[m],x=m*h,eq);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiNJIm1HRiUsJiomLCgmSSJ5R0YlNiMsJkYnIiIiRi9GL0YvKiYiIiNGLyZGLEYmRi8hIiImRiw2IywmRidGL0YvRjNGL0YvKUkiaEdGJUYxRjNGLyooSSNQZUdGJUYvLCZGMkYvRjRGM0YvRjhGM0Yz">LCYqJiwoJkkieUc2IjYjLCZJIm1HRiciIiJGK0YrRismRiY2I0YqISIjJkYmNiMsJkYqRishIiJGK0YrRitJImhHRidGLkYrKihJI1BlR0YnRissJkYsRitGL0YyRitGM0YyRjI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> A 'for loop' can be written for the interior node points as</Text-field>
</Input>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do Eq[i]:=subs(m=i,Eq[m]);od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiIsJiomLCgmSSJ5R0YlNiMiIiNGJyomRi5GJyZGLEYmRichIiImRiw2IyIiIUYnRicpSSJoR0YlRi5GMUYnKihJI1BlR0YlRicsJkYwRidGMkYxRidGNkYxRjE=">LCYqJiwoJkkieUc2IjYjIiIjIiIiJkYmNiNGKiEiIyZGJjYjIiIhRipGKkkiaEdGJ0YtRioqKEkjUGVHRidGKiwmRitGKkYuISIiRipGMUY1RjU=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiMsJiomLCgmSSJ5R0YlNiMiIiQiIiIqJkYnRi8mRixGJkYvISIiJkYsNiNGL0YvRi8pSSJoR0YlRidGMkYvKihJI1BlR0YlRi8sJkYxRi9GM0YyRi9GNkYyRjI=">LCYqJiwoJkkieUc2IjYjIiIkIiIiJkYmNiMiIiMhIiMmRiY2I0YqRipGKkkiaEdGJ0YuRioqKEkjUGVHRidGKiwmRitGKkYvISIiRipGMUY1RjU=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiQsJiomLCgmSSJ5R0YlNiMiIiUiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjRjFGL0YvKUkiaEdGJUYxRjNGLyooSSNQZUdGJUYvLCZGMkYvRjRGM0YvRjdGM0Yz">LCYqJiwoJkkieUc2IjYjIiIlIiIiJkYmNiMiIiQhIiMmRiY2IyIiI0YqRipJImhHRidGLkYqKihJI1BlR0YnRiosJkYrRipGLyEiIkYqRjJGNkY2</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiUsJiomLCgmSSJ5R0YlNiMiIiYiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiIkRi9GLylJImhHRiVGMUYzRi8qKEkjUGVHRiVGLywmRjJGL0Y0RjNGL0Y4RjNGMw==">LCYqJiwoJkkieUc2IjYjIiImIiIiJkYmNiMiIiUhIiMmRiY2IyIiJEYqRipJImhHRidGLkYqKihJI1BlR0YnRiosJkYrRipGLyEiIkYqRjJGNkY2</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq[0]:=y[0]=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiEvJkkieUdGJUYmIiIi">LyZJInlHNiI2IyIiISIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq[N+1]:=y[N+1]=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiYvJkkieUdGJUYmIiIh">LyZJInlHNiI2IyIiJiIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">y[0]:=solve(Eq[0],y[0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJInlHNiI2IyIiISIiIg==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">y[N+1]:=solve(Eq[N+1],y[N+1]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJInlHNiI2IyIiJiIiIQ==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" 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="PkkiaEc2IiMiIiIiIiY=">IyIiIiIiJg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i 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="PiZJI0VxRzYiNiMiIiIsKiomIiNERicmSSJ5R0YlNiMiIiNGJ0YnKiYiI11GJyZGLEYmRichIiJGKkYnKigiIiZGJ0kjUGVHRiVGJywmRjFGJ0YnRjJGJ0Yy">LComSSJ5RzYiNiMiIiMiI0QmRiQ2IyIiIiEjXUYoRisqJkkjUGVHRiVGKywmRilGKyEiIkYrRishIiY=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiMsKiomIiNEIiIiJkkieUdGJTYjIiIkRitGKyomIiNdRismRi1GJkYrISIiKiZGKkYrJkYtNiNGK0YrRisqKCIiJkYrSSNQZUdGJUYrLCZGMkYrRjVGM0YrRjM=">LComSSJ5RzYiNiMiIiQiI0QmRiQ2IyIiIyEjXSZGJDYjIiIiRigqJkkjUGVHRiVGLywmRilGL0YtISIiRi8hIiY=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiQsKiomIiNEIiIiJkkieUdGJTYjIiIlRitGKyomIiNdRismRi1GJkYrISIiKiZGKkYrJkYtNiMiIiNGK0YrKigiIiZGK0kjUGVHRiVGKywmRjJGK0Y1RjNGK0Yz">LComSSJ5RzYiNiMiIiUiI0QmRiQ2IyIiJCEjXSZGJDYjIiIjRigqJkkjUGVHRiUiIiIsJkYpRjJGLSEiIkYyISIm</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiUsKComIiNdIiIiJkkieUdGJUYmRishIiIqJiIjREYrJkYtNiMiIiRGK0YrKigiIiZGK0kjUGVHRiVGKywmRixGK0YxRi5GK0Yu">LCgmSSJ5RzYiNiMiIiUhI10mRiQ2IyIiJCIjRComSSNQZUdGJSIiIiwmRiNGL0YpISIiRi8hIiY=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=[seq(Eq[i],i=1..N)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFzRzYiNyYsKiomIiNEIiIiJkkieUdGJDYjIiIjRilGKSomIiNdRikmRis2I0YpRikhIiJGKEYpKigiIiZGKUkjUGVHRiRGKSwmRjBGKUYpRjJGKUYyLCoqJkYoRikmRis2IyIiJEYpRikqJkYvRilGKkYpRjIqJkYoRilGMEYpRikqKEY0RilGNUYpLCZGKkYpRjBGMkYpRjIsKiomRihGKSZGKzYjIiIlRilGKSomRi9GKUY5RilGMkYnRikqKEY0RilGNUYpLCZGOUYpRipGMkYpRjIsKComRi9GKUZCRilGMkY4RikqKEY0RilGNUYpLCZGQkYpRjlGMkYpRjI=">NyYsKiZJInlHNiI2IyIiIyIjRCZGJTYjIiIiISNdRilGLComSSNQZUdGJkYsLCZGKkYsISIiRixGLCEiJiwqJkYlNiMiIiRGKUYkRi1GKkYpKiZGL0YsLCZGJEYsRipGMUYsRjIsKiZGJTYjIiIlRilGNEYtRiRGKSomRi9GLCwmRjRGLEYkRjFGLEYyLChGOkYtRjRGKSomRi9GLCwmRjpGLEY0RjFGLEYy</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=[seq(y[i],i=1..N)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkldmFyc0c2IjcmJkkieUdGJDYjIiIiJkYnNiMiIiMmRic2IyIiJCZGJzYjIiIl">NyYmSSJ5RzYiNiMiIiImRiQ2IyIiIyZGJDYjIiIkJkYkNiMiIiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=genmatrix(eqs,vars,'B1');</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQUc2Ii1JJ21hdHJpeEdGJDYjNyY3JiwmIiNdISIiKiYiIiYiIiJJI1BlR0YkRi9GLCIjRCIiIUYyNyYsJkYxRi9GLUYvRipGMUYyNyZGMkY0RipGMTcmRjJGMkY0Rio=">PTYiNiQ7IiIiIiIlRiVFXFtsMTYkIiIkRiosJiEjXUYmSSNQZUdGIyEiJjYkRiZGJkYrNiQiIiNGJiwmIiNERiZGLSIiJjYkRipGJ0YzNiRGJkYqIiIhNiRGJ0YnRis2JEYxRipGMzYkRidGMUY3NiRGJ0YqRjI2JEYmRidGNzYkRjFGJ0Y3NiRGMUYxRis2JEYqRiZGNzYkRiZGMUYzNiRGJ0YmRjc2JEYqRjFGMg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalm(B1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkndmVjdG9yRzYiNiM3JiwmIiNEISIiKiYiIiYiIiJJI1BlR0YkRixGKSIiIUYuRi4=">PTYiNiM7IiIiIiIlRVxbbCVGJiwmISNERiZJI1BlR0YjISImIiIjIiIhIiIkRi5GJ0Yu</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> Maple generates a row vector which can be converted to a column vector as:</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">B:=matrix(N,1):for i to N do B[i,1]:=B1[i]:od:evalm(B);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUknbWF0cml4RzYiNiM3JjcjLCYiI0QhIiIqJiIiJiIiIkkjUGVHRiRGLUYqNyMiIiFGL0Yv">PTYiNiQ7IiIiIiIlO0YmRiZFXFtsJTYkRiZGJiwmISNERiZJI1BlR0YjISImNiQiIiNGJiIiITYkIiIkRiZGMTYkRidGJkYx</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> The solution is obtained as:</Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">X:=evalm(inverse(A)&amp;*B);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiWEc2Ii1JJ21hdHJpeEdGJDYjNyY3IywkKiojIiIiIiImRi0sKiIkKyZGLSomIiRdIkYtSSNQZUdGJEYtRi0qJiIjP0YtKUYzIiIjRi1GLSokKUYzIiIkRi1GLUYtLCwiJURKRi0qJiIlXTdGLUYzRi1GLSomIiRdI0YtRjZGLUYtKiYiI0RGLUY5Ri1GLSokKUYzIiIlRi1GLSEiIiwmRkJGRiomRi5GLUYzRi1GRkYtRkY3IywkKipGLEYtLCpGOEYtRjRGLUYxRi0iJHYkRi1GLUY7RkZGR0YtRkY3IywkKipGLEYtLCpGOEYtRjRGLSomIiREIkYtRjNGLUYtRkBGLUYtRjtGRkZHRi1GRjcjLCQqKkYsRi0sKkY4Ri0qJiIjOkYtRjZGLUYtKiYiI3ZGLUYzRi1GLUZTRi1GLUY7RkZGR0YtRkY=">PTYiNiQ7IiIiIiIlO0YmRiZFXFtsJTYkRiZGJiwkKigsKiIkKyZGJkkjUGVHRiMiJF0iKiRGLyIiIyIjPyokRi8iIiRGJkYmLCwiJURKRiZGLyIlXTdGMSIkXSNGNCIjRCokRi9GJ0YmISIiLCYhI0RGJkYvISImRiYjRjwiIiY2JEYyRiYsJCooLCpGNEYmRjFGM0YvRjAiJHYkRiZGJkY2RjxGPUYmRkA2JEY1RiYsJCooLCpGNEYmRjFGM0YvIiREIkY5RiZGJkY2RjxGPUYmRkA2JEYnRiYsJCooLCpGNEYmRjEiIzpGLyIjdkZLRiZGJkY2RjxGPUYmRkA=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" 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="PkkiaEc2IiMiIiIiIiY=">IyIiIiIiJg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do y[i]:=X[i,1];od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJInlHNiI2IyIiIiwkKiojRiciIiZGJywqIiQrJkYnKiYiJF0iRidJI1BlR0YlRidGJyomIiM/RicpRjAiIiNGJ0YnKiQpRjAiIiRGJ0YnRicsLCIlREpGJyomIiVdN0YnRjBGJ0YnKiYiJF0jRidGM0YnRicqJiIjREYnRjZGJ0YnKiQpRjAiIiVGJ0YnISIiLCZGP0ZDKiZGK0YnRjBGJ0ZDRidGQw==">LCQqKCwqIiQrJiIiIkkjUGVHNiIiJF0iKiRGJyIiIyIjPyokRiciIiRGJkYmLCwiJURKRiZGJyIlXTdGKiIkXSNGLSIjRCokRiciIiVGJiEiIiwmISNERiZGJyEiJkYmI0Y2IiIm</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJInlHNiI2IyIiIywkKiojIiIiIiImRissKiokKUkjUGVHRiUiIiRGK0YrKiYiIz9GKylGMEYnRitGKyomIiRdIkYrRjBGK0YrIiR2JEYrRissLCIlREpGKyomIiVdN0YrRjBGK0YrKiYiJF0jRitGNEYrRisqJiIjREYrRi9GK0YrKiQpRjAiIiVGK0YrISIiLCZGP0ZDKiZGLEYrRjBGK0ZDRitGQw==">LCQqKCwqKiRJI1BlRzYiIiIkIiIiKiRGJiIiIyIjP0YmIiRdIiIkdiRGKUYpLCwiJURKRilGJiIlXTdGKiIkXSNGJSIjRCokRiYiIiVGKSEiIiwmISNERilGJiEiJkYpI0Y2IiIm</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJInlHNiI2IyIiJCwkKiojIiIiIiImRissKiokKUkjUGVHRiVGJ0YrRisqJiIjP0YrKUYwIiIjRitGKyomIiREIkYrRjBGK0YrIiRdI0YrRissLCIlREpGKyomIiVdN0YrRjBGK0YrKiZGN0YrRjNGK0YrKiYiI0RGK0YvRitGKyokKUYwIiIlRitGKyEiIiwmRj5GQiomRixGK0YwRitGQkYrRkI=">LCQqKCwqKiRJI1BlRzYiIiIkIiIiKiRGJiIiIyIjP0YmIiREIiIkXSNGKUYpLCwiJURKRilGJiIlXTdGKkYuRiUiI0QqJEYmIiIlRikhIiIsJiEjREYpRiYhIiZGKSNGNSIiJg==</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJInlHNiI2IyIiJSwkKiojIiIiIiImRissKiokKUkjUGVHRiUiIiRGK0YrKiYiIzpGKylGMCIiI0YrRisqJiIjdkYrRjBGK0YrIiREIkYrRissLCIlREpGKyomIiVdN0YrRjBGK0YrKiYiJF0jRitGNEYrRisqJiIjREYrRi9GK0YrKiQpRjBGJ0YrRishIiIsJkZARkMqJkYsRitGMEYrRkNGK0ZD">LCQqKCwqKiRJI1BlRzYiIiIkIiIiKiRGJiIiIyIjOkYmIiN2IiREIkYpRiksLCIlREpGKUYmIiVdN0YqIiRdI0YlIiNEKiRGJiIiJUYpISIiLCYhI0RGKUYmISImRikjRjYiIiY=</Equation></Text-field>
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<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">y[0]:=eval(y[0]);y[N+1]:=eval(y[N+1]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJInlHNiI2IyIiISIiIg==">IiIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJInlHNiI2IyIiJiIiIQ==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ya:=(exp(Pe)-exp(Pe*x))/(exp(Pe)-1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjeWFHNiIqJiwmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJI1BlR0YkIiIiLUYoNiMqJkYtRi5JInhHRiRGLiEiIkYuLCZGJ0YuRi5GM0Yz">KiYsJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSNQZUdGKSIiIi1GJTYjKiZGK0YsSSJ4R0YpRiwhIiJGLCwmRiRGLEYxRixGMQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p1:=plot([seq([i*h,subs(Pe=1,y[i])],i=0..N+1)],thickness=4,color=blue,axes=boxed):</Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p2:=plot(subs(Pe=1,ya),x=0..1,thickness=5,color=brown,axes=boxed,linestyle=2):</Text-field>
</Input>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pt:=textplot([.5,.5,&quot;Pe=1&quot;]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjcHRHNiItSS9JTlRFUkZBQ0VfUExPVEdGJDYjLUklVEVYVEdGJDYkNyQkIiImISIiRixRJVBlPTFGJA==">LSUlUExPVEc2Iy1JJVRFWFRHNiI2JDckJCIiJiEiIkYqUSVQZT0xRic=</Equation></Text-field>
</Output>
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<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({p1,p2,pt},title=&quot;Figure Exp. 3.1.11.&quot;,labels=[x,&quot;y&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, 4352 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p1:=plot([seq([i*h,subs(Pe=50,y[i])],i=0..N+1)],thickness=4,color=green,axes=boxed):</Text-field>
</Input>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p2:=plot(subs(Pe=50,ya),x=0..1,thickness=5,color=brown,axes=boxed,linestyle=2):</Text-field>
</Input>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pt:=textplot([.5,.5,&quot;Pe=50&quot;]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjcHRHNiItSS9JTlRFUkZBQ0VfUExPVEdGJDYjLUklVEVYVEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYkNyQkIiImISIiRi9RJlBlPTUwRiQ=">LSUlUExPVEc2Iy1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDckJCIiJiEiIkYtUSZQZT01MEYq</Equation></Text-field>
</Output>
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<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({p1,p2,pt},title=&quot;Figure Exp. 3.1.12.&quot;,labels=[x,&quot;y&quot;]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">[encoded data, 5012 characters]</Plot></Text-field>
</Output>
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<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We observe that when the forward difference accurate to the order h2 is used, even when the  Peclet number is 1, there is a slight discrepancy between the finite difference solution and the analytical solution.  However, when the Peclet number is high (Pe = 50) the forward difference scheme does not five an unrealistic oscillation like the central difference scheme.  Note that for three digit accuracy with the analytical solution, N = 40 and 110 interior note points are required for central difference and forward difference approximations, respectively.</Text-field>
</Input>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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</Worksheet>