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    </Task-category>
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    </Annotation-category>
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<Group labelreference="L107" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Example 6.1 N2</Text-field>
</Input>
</Group>
<Group labelreference="L106" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group>
<Group labelreference="L83" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the governing equation:</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ge:=diff(u(x,y),y$2)=-epsilon^2*diff(u(x,y),x$2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZ2VHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkieUdGJC1JIiRHRig2JEYuIiIjLCQqJilJKGVwc2lsb25HRiRGMiIiIi1GJzYkRiotRjA2JEYtRjJGNyEiIg==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC1JInVHNiI2JEkieEdGK0kieUdGK0YuRi4sJComSShlcHNpbG9uR0YrIiIjLUYkNiQtRiQ2JEYpRi1GLSIiIiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L84" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the boundary conditions:</Text-field>
</Input>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=u(x,y)-0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLUkidUdGJDYkSSJ4R0YkSSJ5R0Yk">LUkidUc2IjYkSSJ4R0YkSSJ5R0Yk</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=u(x,y)-0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLUkidUdGJDYkSSJ4R0YkSSJ5R0Yk">LUkidUc2IjYkSSJ4R0YkSSJ5R0Yk</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc3:=u(x,y)-0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMzRzYiLUkidUdGJDYkSSJ4R0YkSSJ5R0Yk">LUkidUc2IjYkSSJ4R0YkSSJ5R0Yk</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc4:=u(x,y)-1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmM0RzYiLCYtSSJ1R0YkNiRJInhHRiRJInlHRiQiIiJGKyEiIg==">LCYtSSJ1RzYiNiRJInhHRiVJInlHRiUiIiIhIiJGKQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">epsilon:=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkoZXBzaWxvbkc2IiIiIg==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L85" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the finite difference approximations for the derivatives:</Text-field>
</Input>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxf:=1/2/h*(-u[m+2](zeta)-3*u[m](zeta)+4*u[m+1](zeta));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGZHNiIsJCooIyIiIiIiI0YoSSJoR0YkISIiLCgtJkkidUdGJDYjLCZJIm1HRiRGKEYpRig2I0klemV0YUdGJEYrKiYiIiRGKC0mRi82I0YyRjNGKEYrKiYiIiVGKC0mRi82IywmRjJGKEYoRihGM0YoRihGKEYo">LCQqJkkiaEc2IiEiIiwoLSZJInVHRiU2IywmSSJtR0YlIiIiIiIjRi42I0klemV0YUdGJUYmLSZGKjYjRi1GMCEiJC0mRio2IywmRi1GLkYuRi5GMCIiJUYuI0YuRi8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxb:=1/2/h*(u[m-2](zeta)+3*u[m](zeta)-4*u[m-1](zeta));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGJHNiIsJCooIyIiIiIiI0YoSSJoR0YkISIiLCgtJkkidUdGJDYjLCZJIm1HRiRGKEYpRis2I0klemV0YUdGJEYoKiYiIiRGKC0mRi82I0YyRjNGKEYoKiYiIiVGKC0mRi82IywmRjJGKEYoRitGM0YoRitGKEYo">LCQqJkkiaEc2IiEiIiwoLSZJInVHRiU2IywmSSJtR0YlIiIiISIjRi42I0klemV0YUdGJUYuLSZGKjYjRi1GMCIiJC0mRio2IywmRi1GLkYmRi5GMCEiJUYuI0YuIiIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydx:=1/2/h*(u[m+1](zeta)-u[m-1](zeta));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklZHlkeEc2IiwkKigjIiIiIiIjRihJImhHRiQhIiIsJi0mSSJ1R0YkNiMsJkkibUdGJEYoRihGKDYjSSV6ZXRhR0YkRigtJkYvNiMsJkYyRihGKEYrRjNGK0YoRig=">LCQqJkkiaEc2IiEiIiwmLSZJInVHRiU2IywmSSJtR0YlIiIiRi5GLjYjSSV6ZXRhR0YlRi4tJkYqNiMsJkYtRi5GJkYuRi9GJkYuI0YuIiIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">d2ydx2:=1/h^2*(u[m-1](zeta)-2*u[m](zeta)+u[m+1](zeta));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknZDJ5ZHgyRzYiKiYpSSJoR0YkIiIjISIiLCgtJkkidUdGJDYjLCZJIm1HRiQiIiJGMUYpNiNJJXpldGFHRiRGMSomRihGMS0mRi02I0YwRjJGMUYpLSZGLTYjLCZGMEYxRjFGMUYyRjFGMQ==">KiZJImhHNiIhIiMsKC0mSSJ1R0YkNiMsJkkibUdGJCIiIiEiIkYtNiNJJXpldGFHRiRGLS0mRik2I0YsRi9GJS0mRik2IywmRixGLUYtRi1GL0YtRi0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L86" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Convert the boundary conditions to finite difference form:</Text-field>
</Input>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=subs(diff(u(x,y),x)=subs(m=0,dydxf),u(x,y)=u[0](zeta),x=0,bc1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLSZJInVHRiQ2IyIiITYjSSV6ZXRhR0Yk">LSZJInVHNiI2IyIiITYjSSV6ZXRhR0Yl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=subs(diff(u(x,y),x)=subs(m=N+1,dydxb),u(x,y)=u[N+1](zeta),x=1,bc2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLSZJInVHRiQ2IywmSSJOR0YkIiIiRitGKzYjSSV6ZXRhR0Yk">LSZJInVHNiI2IywmSSJOR0YlIiIiRilGKTYjSSV6ZXRhR0Yl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L87" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the number of interior node points:</Text-field>
</Input>
</Group>
<Group labelreference="L16" 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="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="PiZJI2VxRzYiNiMiIiEtJkkidUdGJUYmNiNJJXpldGFHRiU=">LSZJInVHNiI2IyIiITYjSSV6ZXRhR0Yl</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="PiZJI2VxRzYiNiMiIiQtJkkidUdGJUYmNiNJJXpldGFHRiU=">LSZJInVHNiI2IyIiJDYjSSV6ZXRhR0Yl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L88" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Convert the governing equation to finite difference from (equation 6.1.12):</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[N+1+i]:=diff(u[N+1+i](zeta),zeta)= subs(diff(u(x,y),x$2) = subs(m=i,d2ydx2),diff(u(x,y),x) = subs(m=i,dydx),u(x,y)=u[i](zeta),x=i*h,rhs(h^2/epsilon^2*ge));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0klemV0YUdGJUYxLCgtJkYvNiMiIiFGMCEiIiomIiIjIiIiLSZGLzYjRjpGMEY6RjotJkYvNiNGOUYwRjc=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIlNiNJJXpldGFHRipGLiwoLSZGKTYjIiIhRi0hIiItJkYpNiMiIiJGLSIiIy0mRik2I0Y5Ri1GNA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiYvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0klemV0YUdGJUYxLCgtJkYvNiMiIiJGMCEiIiomIiIjRjYtJkYvNiNGOUYwRjZGNi0mRi82IyIiJEYwRjc=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiImNiNJJXpldGFHRipGLiwoLSZGKTYjIiIiRi0hIiItJkYpNiMiIiNGLUY4LSZGKTYjIiIkRi1GNA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L89" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the boundary values:</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u[0](zeta):=(solve(eq[0],u[0](zeta)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiE2I0klemV0YUdGJkYo">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u[N+1](zeta):=solve(eq[N+1],u[N+1](zeta));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiQ2I0klemV0YUdGJiIiIQ==">IiIh</Equation></Text-field>
</Output>
</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]:=diff(u[i](zeta),zeta)=u[N+1+i](zeta);od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0klemV0YUdGJUYxLSZGLzYjIiIlRjA=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIiNiNJJXpldGFHRipGLi0mRik2IyIiJUYt</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0klemV0YUdGJUYxLSZGLzYjIiImRjA=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIjNiNJJXpldGFHRipGLi0mRik2IyIiJkYt</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N do eq[i]:=eval(eq[i]);od;for i from 1 to N do eq[N+1+i]:=eval(eq[N+1+i]);od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0klemV0YUdGJUYxLSZGLzYjIiIlRjA=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIiNiNJJXpldGFHRipGLi0mRik2IyIiJUYt</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0klemV0YUdGJUYxLSZGLzYjIiImRjA=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIjNiNJJXpldGFHRipGLi0mRik2IyIiJkYt</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0klemV0YUdGJUYxLCYqJiIiIyIiIi0mRi82I0Y1RjBGNUY1LSZGLzYjRjRGMCEiIg==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIlNiNJJXpldGFHRipGLiwmLSZGKTYjIiIiRi0iIiMtJkYpNiNGNEYtISIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiYvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0klemV0YUdGJUYxLCYtJkYvNiMiIiJGMCEiIiomIiIjRjYtJkYvNiNGOUYwRjZGNg==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiImNiNJJXpldGFHRipGLiwmLSZGKTYjIiIiRi0hIiItJkYpNiMiIiNGLUY4</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L92" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Generate the A matrix using the governing equations and the dependent variables</Text-field>
</Input>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqns:=[seq(rhs(eq[j]),j=1..N),seq(rhs(eq[N+1+j]),j=1..N)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklZXFuc0c2IjcmLSZJInVHRiQ2IyIiJTYjSSV6ZXRhR0YkLSZGKDYjIiImRissJiomIiIjIiIiLSZGKDYjRjRGK0Y0RjQtJkYoNiNGM0YrISIiLCZGNUY7KiZGM0Y0RjhGNEY0">NyYtJkkidUc2IjYjIiIlNiNJJXpldGFHRiYtJkYlNiMiIiZGKSwmLSZGJTYjIiIiRikiIiMtJkYlNiNGNEYpISIiLCZGMEY4RjVGNA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=[seq(u[i](zeta),i=1..N),seq(u[N+1+i](zeta),i=1..N)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiWUc2IjcmLSZJInVHRiQ2IyIiIjYjSSV6ZXRhR0YkLSZGKDYjIiIjRistJkYoNiMiIiVGKy0mRig2IyIiJkYr">NyYtJkkidUc2IjYjIiIiNiNJJXpldGFHRiYtJkYlNiMiIiNGKS0mRiU2IyIiJUYpLSZGJTYjIiImRik=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=genmatrix(eqns,Y,'b1');</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQUc2Ii1JJ21hdHJpeEdGJDYjNyY3JiIiIUYqIiIiRio3JkYqRipGKkYrNyYiIiMhIiJGKkYqNyZGL0YuRipGKg==">PTYiNiQ7IiIiIiIlRiVFXFtsMTYkRiYiIiMiIiE2JEYmRiZGKzYkRidGJ0YrNiRGJiIiJEYmNiRGJ0YvRis2JEYvRiZGKjYkRi9GKiEiIjYkRidGJkYzNiRGJkYnRis2JEYnRipGKjYkRipGJ0YmNiRGKkYqRis2JEYvRidGKzYkRipGL0YrNiRGL0YvRis2JEYqRiZGKw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L93" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Convert the entries of the A matrix as decimals if N is greater than two (as in chapter 5.1):</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">if N&gt;2 then A:=map(evalf,A):end;</Text-field>
</Input>
</Group>
<Group labelreference="L103" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="`:=`(NRow, rowdim(A));" display="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">QyQ+SSVOUm93RzYiLUkncm93ZGltR0YlNiNJIkFHRiUiIiI=</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklTlJvd0c2IiIiJQ==">IiIl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L105" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field style="Error" layout="Error">Error, illegal use of an object as a name</Text-field>
<Text-field style="Error" layout="Maple Output"><Equation executable="false">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" 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="LUknbWF0cml4RzYiNiM3JjcmIiIhRigiIiJGKDcmRihGKEYoRik3JiIiIyEiIkYoRig3JkYtRixGKEYo">PTYiNiQ7IiIiIiIlRiVFXFtsMTYkRiYiIiMiIiE2JEYmRiZGKzYkRidGJ0YrNiRGJiIiJEYmNiRGJ0YvRis2JEYvRiZGKjYkRi9GKiEiIjYkRidGJkYzNiRGJkYnRis2JEYnRipGKjYkRipGJ0YmNiRGKkYqRis2JEYvRidGKzYkRipGL0YrNiRGL0YvRis2JEYqRiZGKw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b:=matrix(2*N,1):for i from 1 to 2*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="LUknbWF0cml4RzYiNiM3JjcjIiIhRidGJ0Yn">PTYiNiQ7IiIiIiIlO0YmRiZFXFtsJTYkRiZGJiIiITYkIiIkRiZGKzYkRidGJkYrNiQiIiNGJkYr</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L95" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Note that for the example given the b vector is zero.  However, depending on the boundary conditions, bc3 and bc3, the b vector can be a function of \316\266 or a constant vector.</Font></Text-field>
</Input>
</Group>
<Group labelreference="L30" 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="PkkiaEc2IiMiIiIiIiQ=">IyIiIiIiJA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">J:=jordan(A,S);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiSkc2Ii1JJ21hdHJpeEdGJDYjNyY3JiEiIiIiIUYrRis3JkYrIiIiRitGKzcmRitGKyokKSIiJCNGLSIiI0YtRis3JkYrRitGKywkRi9GKg==">PTYiNiQ7IiIiIiIlRiVFXFtsMTYkRiYiIiMiIiE2JEYmRiYhIiI2JEYnRicsJCokIiIkI0YmRipGLTYkRiZGMUYrNiRGJ0YxRis2JEYxRiZGKzYkRjFGKkYrNiRGJ0YmRis2JEYmRidGKzYkRidGKkYrNiRGKkYnRis2JEYqRipGJjYkRjFGJ0YrNiRGKkYxRis2JEYxRjFGMDYkRipGJkYr</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=evalm(S&amp;*exponential(J,zeta)&amp;*inverse(S)):</Text-field>
</Input>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat1:=evalm(subs(zeta=zeta-zeta1,evalm(mat))):</Text-field>
</Input>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b2:=evalm(subs(zeta=zeta1,evalm(b))):</Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat2:=evalm(mat1&amp;*b2):</Text-field>
</Input>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat2:=map(expand,mat2):</Text-field>
</Input>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat3:=map(int,mat2,zeta1=0..zeta):</Text-field>
</Input>
</Group>
<Group labelreference="L96" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The initial condition vector is defined here.</Text-field>
</Input>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y0:=matrix(2*N,1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjWTBHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIiU7RipGKjci">PTYiNiQ7IiIiIiIlO0YmRiZFXFtsIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do Y0[i,1]:=p[i];od:</Text-field>
</Input>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do Y0[N+i,1]:=c[i]:od:</Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalm(Y0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUknbWF0cml4RzYiNiM3JjcjJkkicEdGJDYjIiIiNyMmRik2IyIiIzcjJkkiY0dGJEYqNyMmRjJGLg==">PTYiNiQ7IiIiIiIlO0YmRiZFXFtsJTYkRiZGJiZJInBHRiM2I0YmNiQiIiRGJiZJImNHRiNGLTYkRidGJiZGMTYjIiIjNiRGNUYmJkYsRjQ=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L97" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution is found by adding the nonhomogeneous part to the homogeneous part.</Text-field>
</Input>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=evalm(mat&amp;*Y0+mat3):</Text-field>
</Input>
</Group>
<Group labelreference="L98" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution at y = 0 and y = 1 is stored in sol0 and sol1 to calculate the unknown constants.</Text-field>
</Input>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol0:=map(eval,evalm(subs(zeta=0,evalm(Y)))):</Text-field>
</Input>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol1:=map(eval,evalm(subs(zeta=epsilon/h,evalm(Y)))):</Text-field>
</Input>
</Group>
<Group labelreference="L99" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Now the boundary conditions bc3 and bc4 are applied.</Text-field>
</Input>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do Eq[i]:=subs(diff(u(x,y),y)=epsilon/h*c[i],u(x,y)=p[i],x=i*h,bc3);od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiImSSJwR0YlRiY=">JkkicEc2IjYjIiIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiMmSSJwR0YlRiY=">JkkicEc2IjYjIiIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do Eq[N+i]:=evalf(subs(diff(u(x,y),y)=epsilon/h*sol1[N+i,1],u(x,y)=sol1[i,1],bc4));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiQsLComJCIrRVkjeiwmISIpIiIiJkkicEdGJTYjRi1GLUYtKiYkIitFJWU2LCVGLEYtJkYvNiMiIiNGLSEiIiomJCIrW2M/MkpGLEYtJkkiY0dGJUYwRi1GLSomJCIrYyI9YTUjRixGLSZGPEY1Ri1GNyRGLSIiIUY3">LCwmSSJwRzYiNiMiIiIkIitFWSN6LCYhIikmRiQ2IyIiIyQhK0UlZTYsJUYqJkkiY0dGJUYmJCIrW2M/MkpGKiZGMUYsJCErYyI9YTUjRiokISIiIiIhRic=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiUsLComJCIrRSVlNiwlISIpIiIiJkkicEdGJTYjRi1GLSEiIiomJCIrRVkjeiwmRixGLSZGLzYjIiIjRi1GLSomJCIrYyI9YTUjRixGLSZJImNHRiVGMEYtRjEqJiQiK1tjPzJKRixGLSZGPEY2Ri1GLSRGLSIiIUYx">LCwmSSJwRzYiNiMiIiIkIStFJWU2LCUhIikmRiQ2IyIiIyQiK0VZI3osJkYqJkkiY0dGJUYmJCErYyI9YTUjRiomRjFGLCQiK1tjPzJKRiokISIiIiIhRic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L101" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The unknown constants are solved as:</Text-field>
</Input>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">csol:=solve({seq(Eq[i],i=1..2*N)},{seq(c[i],i=1..N),seq(p[i],i=1..N)});</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklY3NvbEc2IjwmLyZJImNHRiQ2IyIiIyQiK3VwOiMpKiohIzYvJkYoNiMiIiJGKy8mSSJwR0YkRjAkIiIhRjYvJkY0RilGNQ==">PCYvJkkiY0c2IjYjIiIjJCIrdXA6IykqKiEjNi8mRiU2IyIiIkYpLyZJInBHRiZGLiQiIiFGNC8mRjJGJ0Yz</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">assign(csol);</Text-field>
</Input>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=map(eval,Y):</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 do u[i](zeta):=eval((Y[i,1]));od:</Text-field>
</Input>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 do u[i](zeta):=eval(u[i](zeta));od:</Text-field>
</Input>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 do u[i](y):=eval(subs(zeta=epsilon*y/h,u[i](zeta)));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiE2I0kieUdGJkYo">IiIh</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiI2I0kieUdGJiwmKiokIit1cDojKSoqISM2RigtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IywkKiYiIiRGKEYqRighIiJGKCwmRihGKCokKUY4I0YoIiIjRihGKEY5LCZGO0YoRihGOUY5RjkqJiQiKylbeTUqXEYvRigtRjE2IywkRjdGKEYoRig=">LCYqKC1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCRJInlHRikhIiQiIiIsJkYuRi4qJCIiJCNGLiIiI0YuISIiLCZGMEYuRjRGLkY0JCErdXA6IykqKiEjNi1GJTYjLCRGLEYxJCIrKVt5NSpcRjg=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiM2I0kieUdGJiwmKiokIit1cDojKSoqISM2IiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMsJComIiIkRjBGKkYwISIiRjAsJkYwRjAqJClGOSNGMEYoRjBGMEY6LCZGPEYwRjBGOkY6RjoqJiQiKylbeTUqXEYvRjAtRjI2IywkRjhGMEYwRjA=">LCYqKC1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCRJInlHRikhIiQiIiIsJkYuRi4qJCIiJCNGLiIiI0YuISIiLCZGMEYuRjRGLkY0JCErdXA6IykqKiEjNi1GJTYjLCRGLEYxJCIrKVt5NSpcRjg=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiQ2I0kieUdGJiIiIQ==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L102" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Hence, the semianalytical solution is obtained for temperature distribution.  The plots obtained for N=10 node points is given below:</Text-field>
</Input>
</Group>
<Group labelreference="L79" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 do
  pl[i]:=line([0.3,0.98-abs(i-5.25)*0.14],[0.6,evalf(subs(y=0.6,u[i](y)))],thickness=1,linestyle=dot);
  pt[i]:=textplot([0.3,0.98-abs(i-5.25)*0.14,typeset(u[i],&quot;(y)&quot;)],align=left):
end do:</Text-field>
</Input>
</Group>
<Group labelreference="L67" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pp:=plot([seq(u[i](y),i=0..N+1)],y=0..1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjcHBHNiItSS9JTlRFUkZBQ0VfUExPVEdGJDYoLUknQ1VSVkVTRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQ3UzckJCIiIUYxRjA3JCQiM2VtbW07YXJ6QCEjPkYwNyQkIjNbTEwkZTl1aTIlRjVGMDckJCIzbm1tbSJ6XyI0aUY1RjA3JCQiM1ttbW1UJnBoTilGNUYwNyQkIjNDTExlKj0pSFw1ISM9RjA3JCQiM2dtbSJ6LzN1QyJGQkYwNyQkIjMlKSoqKlw3TFJEWCJGQkYwNyQkIjNdbW0ielInb2s7RkJGMDckJCIzdyoqKlxpNWBoKD1GQkYwNyQkIjNXTExMM0VuJDQjRkJGMDckJCIzcW1tOy9SRSZHI0ZCRjA3JCQiMyIpKioqKipcS100XSNGQkYwNyQkIjMkKioqKioqXFBBdnIjRkJGMDckJCIzKSoqKioqKlxuSGkjSEZCRjA3JCQiM2ptbSJ6KmV2OkpGQkYwNyQkIjM/TExMMzQ3VExGQkYwNyQkIjMsTExMTFkuS05GQkYwNyQkIjN3KioqXDdvN1R2JEZCRjA3JCQiMydHTExMUSpvXVJGQkYwNyQkIjNBKytEIj1sajslRkJGMDckJCIzMSsrdlYmUjxQJUZCRjA3JCQiM1dMTCRlOUVnZSVGQkYwNyQkIjNHTExlUiIzR3klRkJGMDckJCIzY21tOy9UMSYqXEZCRjA3JCQiMyZlbTt6UlFiQCZGQkYwNyQkIjNcKioqXCg9PlkyYUZCRjA3JCQiMzltbTt6WHU5Y0ZCRjA3JCQiM2wqKioqKipceSkpR2VGQkYwNyQkIjMnKikqKipcaV9RUWdGQkYwNyQkIjNAKioqXDd5JTNUaUZCRjA3JCQiMzUqKioqXFAhW2hZJ0ZCRjA3JCQiM2tLTEwkUXgkb21GQkYwNyQkIjMhKSoqKioqXFArVilvRkJGMDckJCIzP21tInpwZSp6cUZCRjA3JCQiMyUpKioqKipcI1wnUUgoRkJGMDckJCIzR0tMZTlTOCZcKEZCRjA3JCQiM1IqKipcaT89YnEoRkJGMDckJCIzIkhMTCQzcz82ekZCRjA3JCQiM2EqKipcN2BXbDcpRkJGMDckJCIzI3BtbW0nKlJSTClGQkYwNyQkIjNRbW07YTwuWSYpRkJGMDckJCIzPUxMZTl0T2MoKUZCRjA3JCQiM3UqKioqKipcUWtcKilGQkYwNyQkIjNDTEwkM2RnNjwqRkJGMDckJCIzSW1tbW14R3AkKkZCRjA3JCQiM0ErK0Qib0swZSpGQkYwNyQkIjNBKyt2PTVzI3kqRkJGMDckJCIiIkYxRjAtSSdDT0xPVVJHRiQ2JkkkUkdCR0YkJCIqKysrKyIhIilGMEYwLUYpNiQ3UzckRjAkIjJBIWZoXHApKioqKiohI0c3JEYzJCIzI3BIKj4uOThLbCEjPzckRjckIjNxWipcUitYUEEiRjU3JEY6JCIzR1ZYNzlSPnE9RjU3JEY9JCIzdTFgJlsmKXAnR0RGNTckRkAkIjMhUnNLOVtKVz4kRjU3JEZEJCIzIUhWNTxnW0wjUUY1NyRGRyQiM1MlSFFLcz4pKVslRjU3JEZKJCIzR1lucC0hcFw+JkY1NyRGTSQiMyFwX1IzNSp6PmZGNTckRlAkIjM1b0dQWTxGIXAnRjU3JEZTJCIzNVAjeSEzKipSI1IoRjU3JEZWJCIzKzpVIipmJnpAQClGNTckRlkkIjNRTV8iUmBQKnAhKkY1NyRGZm4kIjNRPypmRCpHdUsqKkY1NyRGaW4kIjNrLiopcHgxKlwyIkZCNyRGXG8kIjNDT3BbM2hxdzZGQjckRl9vJCIzb1ZdP11JMW43RkI3JEZibyQiM1s+dGAiZUB1UCJGQjckRmVvJCIzKXotP3VNJT4hWyJGQjckRmhvJCIzWShlISpRRyEqKSlmIkZCNyRGW3AkIjM5KVJUIUhKOD08RkI3JEZecCQiMylwLF0iW0deXD1GQjckRmFwJCIzcS4mPlplIilvKD5GQjckRmRwJCIzIipcelJZYCtBQEZCNyRGZ3AkIjNpIUhSNCcqcD1HI0ZCNyRGanAkIjNgXXhSLHM4SENGQjckRl1xJCIzW2BGN01IRChmI0ZCNyRGYHEkIjN3LGoiengiXCJ5I0ZCNyRGY3EkIjNfciNIUGVTRyhIRkI3JEZmcSQiM1FEQD9mTDpwSkZCNyRGaXEkIjM+NWcyYT4qM1MkRkI3JEZcciQiM25UWjVSb0pBT0ZCNyRGX3IkIjNnWXNWaiR5TShRRkI3JEZiciQiMzs6bFVDKnpdNiVGQjckRmVyJCIzY0koUWEwdGFSJUZCNyRGaHIkIjNHIkckXDpMImVuJUZCNyRGW3MkIjMpXDAiZUFfNCgpXEZCNyRGXnMkIjNHdT1rK01qNWBGQjckRmFzJCIzVUtUbDhHL3JjRkI3JEZkcyQiMy5eYHU1S19TZ0ZCNyRGZ3MkIjMnW1ZObidRZFVrRkI3JEZqcyQiM1MkXFJZJCllcSdvRkI3JEZddCQiM2l0RyJ5TSk9IkcoRkI3JEZgdCQiM0EvSDgnPkhneShGQjckRmN0JCIzcVA7Xk5uam0jKUZCNyRGZnQkIjNjbXgoRypvRzYpKUZCNyRGaXQkIjMjKjN2P147cmwkKkZCNyRGXHUkIjNHK1IiNCsrKysiISM8LUZfdTYmRmF1JCIpVnlnPkZkdSQiKWRAUiEpRmR1RmBfbC1GKTYkRmd1LUZfdTYmRmF1JCIpJz4hXCYpRmR1JCIpIyllcWtGZHUkIik/IVxEIkZkdS1GKTYkRi4tRl91NiZGYXVGMEYwRmJ1LUkrQVhFU0xBQkVMU0dGJDYkSSJ5R0YkUSFGJC1JJVZJRVdHRio2JDtGMEZcdUkoREVGQVVMVEdGJA==">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L54" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display([pp,seq(pl[i],i=0..N+1),seq(pt[i],i=0..N+1)],axes=boxed,thickness=3,title=&quot;Figure Exp. 6.1.&quot;,labels=[y,&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, 20040 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L55" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">M:=10;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTUc2IiIjNQ==">IiM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T1:=[seq(evalf(i/M),i=0..M)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVDFHNiI3LSQiIiFGJyQiKysrKys1ISM1JCIrKysrKz9GKiQiKysrKytJRiokIisrKysrU0YqJCIrKysrK11GKiQiKysrKytnRiokIisrKysrcUYqJCIrKysrKyEpRiokIisrKysrISpGKiQiIiJGJw==">Ny0kIiIhRiQkIisrKysrNSEjNSQiKysrKys/RickIisrKysrSUYnJCIrKysrK1NGJyQiKysrKytdRickIisrKysrZ0YnJCIrKysrK3FGJyQiKysrKyshKUYnJCIrKysrKyEqRickIiIiRiQ=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for j from 1 to M do P[j]:=plot([seq([h*i,evalf(subs(y=T1[j],evalf(u[i](y))))],i=0..N+1)],style=line,thickness=3,axes=boxed,view=[0..1,0..1.1]):od:</Text-field>
</Input>
</Group>
<Group labelreference="L71" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P[M+1]:=plot([seq([h*i,evalf(subs(x=i*h,1))],i=0..N+1)],style=line,thickness=3,title=&quot;Figure Exp. 6.2.&quot;,axes=boxed):</Text-field>
</Input>
</Group>
<Group labelreference="L82" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for j from 1 to M+1 do
  pt[j]:=textplot([0.5,evalf(subs(y=T1[j],u[5](y))),typeset(y,sprintf(&quot;=%4.2f&quot;,T1[j]))],align=above);
od:</Text-field>
</Input>
</Group>
<Group labelreference="L72" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({seq(P[i],i=1..M+1),seq(pt[j],j=1..M+1)},labels=[x,u]);</Text-field>
</Input>
<Output>
<Text-field style="Error" layout="Error">Error:TEXT location must be numeric; received: [.5, u[5](.3000000000)]</Text-field>
</Output>
</Group>
<Group labelreference="L60" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ny:=30;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjTnlHNiIiI0k=">IiNJ</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L61" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">PP:=matrix(N+2,Ny);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjUFBHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIiU7RioiI0k3Ig==">PTYiNiQ7IiIiIiIlO0YmIiNJRVxbbCE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L62" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to Ny do PP[1,i]:=0;PP[N+2,i]:=0;od:</Text-field>
</Input>
</Group>
<Group labelreference="L63" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N+2 do PP[i,1]:=0;PP[i,Ny]:=1;od:</Text-field>
</Input>
</Group>
<Group labelreference="L64" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 2 to N+1 do for j from 2 to Ny-1 do PP[i,j]:=evalf(subs(y=(j-1)/(Ny-1),u[i-1](y)));od;od:</Text-field>
</Input>
</Group>
<Group labelreference="L65" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plotdata := [seq([ seq([(i-1)/(N+1),(j-1)/(Ny-1),PP[i,j]], i=1..N+2)], j=1..Ny)]:</Text-field>
</Input>
</Group>
<Group labelreference="L66" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">surfdata(plotdata,axes=boxed,title=&quot;Figure Exp. 6.3.&quot;,labels=[x,y,u],orientation=[-120,60] );</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, 5504 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L68" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>