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<Group labelreference="L2" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart;with(linalg):with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L69" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The governing equation and boundary conditions are entered.  Boundary conditions in y are entered with a right hand side.</Text-field>
</Input>
</Group>
<Group labelreference="L3" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ge:=diff(u(x,y),y$2)=diff(u(x,y),y)-diff(u(x,y),x$2)-1/x*diff(u(x,y),x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZ2VHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkieUdGJC1JIiRHRig2JEYuIiIjLCgtRic2JEYqRi4iIiItRic2JEYqLUYwNiRGLUYyISIiKiZGLUY7LUYnNiRGKkYtRjZGOw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC1JInVHNiI2JEkieEdGK0kieUdGK0YuRi4sKEYnIiIiLUYkNiQtRiQ2JEYpRi1GLSEiIiomRi1GNUYzRjBGNQ==</Equation></Text-field>
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<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=u(x,y);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLUkidUdGJDYkSSJ4R0YkSSJ5R0Yk">LUkidUc2IjYkSSJ4R0YkSSJ5R0Yk</Equation></Text-field>
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<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=u(x,y);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLUkidUdGJDYkSSJ4R0YkSSJ5R0Yk">LUkidUc2IjYkSSJ4R0YkSSJ5R0Yk</Equation></Text-field>
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<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc3:=u(x,y)=0;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMzRzYiLy1JInVHRiQ2JEkieEdGJEkieUdGJCIiIQ==">Ly1JInVHNiI2JEkieEdGJUkieUdGJSIiIQ==</Equation></Text-field>
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<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc4:=u(x,y)-1=0;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmM0RzYiLywmLUkidUdGJDYkSSJ4R0YkSSJ5R0YkIiIiRiwhIiIiIiE=">LywmLUkidUc2IjYkSSJ4R0YmSSJ5R0YmIiIiRiohIiIiIiE=</Equation></Text-field>
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<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Pe:=1;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjUGVHNiIiIiI=">IiIi</Equation></Text-field>
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</Group>
<Group labelreference="L10" 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>
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<Group labelreference="L72" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The dimensions of teh domain and the number of interior points are entered:</Text-field>
</Input>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">L:=1;H:=1;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTEc2IiIiIg==">IiIi</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiSEc2IiIiIg==">IiIi</Equation></Text-field>
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<Group labelreference="L73" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Boundary conditions in x and in the governin equaiton are convered to finite-difference form:</Text-field>
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<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">fd1:=1/2/h*(-u[m+2](zeta)-3*u[m](y)+4*u[m+1](y));</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZmQxRzYiLCQqKCMiIiIiIiNGKEkiaEdGJCEiIiwoLSZJInVHRiQ2IywmSSJtR0YkRihGKUYoNiNJJXpldGFHRiRGKyomIiIkRigtJkYvNiNGMjYjSSJ5R0YkRihGKyomIiIlRigtJkYvNiMsJkYyRihGKEYoRjpGKEYoRihGKA==">LCQqKCMiIiIiIiNGJUkiaEc2IiEiIiwoLSZJInVHRig2IywmSSJtR0YoRiVGJkYlNiNJJXpldGFHRihGKSomIiIkRiUtJkYtNiNGMDYjSSJ5R0YoRiVGKSomIiIlRiUtJkYtNiMsJkYwRiVGJUYlRjhGJUYlRiVGJQ==</Equation></Text-field>
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<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bd1:=1/2/h*(u[m-2](y)+3*u[m](y)-4*u[m-1](y));</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmQxRzYiLCQqKCMiIiIiIiNGKEkiaEdGJCEiIiwoLSZJInVHRiQ2IywmSSJtR0YkRihGKUYrNiNJInlHRiRGKComIiIkRigtJkYvNiNGMkYzRihGKComIiIlRigtJkYvNiMsJkYyRihGKEYrRjNGKEYrRihGKA==">LCQqKCMiIiIiIiNGJUkiaEc2IiEiIiwoLSZJInVHRig2IywmSSJtR0YoRiVGJkYpNiNJInlHRihGJSomIiIkRiUtJkYtNiNGMEYxRiVGJSomIiIlRiUtJkYtNiMsJkYwRiVGJUYpRjFGJUYpRiVGJQ==</Equation></Text-field>
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<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cd1:=1/2/h*(u[m+1](y)-u[m-1](zeta));</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkY2QxRzYiLCQqKCMiIiIiIiNGKEkiaEdGJCEiIiwmLSZJInVHRiQ2IywmSSJtR0YkRihGKEYoNiNJInlHRiRGKC0mRi82IywmRjJGKEYoRis2I0klemV0YUdGJEYrRihGKA==">LCQqKCMiIiIiIiNGJUkiaEc2IiEiIiwmLSZJInVHRig2IywmSSJtR0YoRiVGJUYlNiNJInlHRihGJS0mRi02IywmRjBGJUYlRik2I0klemV0YUdGKEYpRiVGJQ==</Equation></Text-field>
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<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cd2:=1/h^2*(u[m-1](zeta)-2*u[m](zeta)+u[m+1](y));</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkY2QyRzYiKiYpSSJoR0YkIiIjISIiLCgtJkkidUdGJDYjLCZJIm1HRiQiIiJGMUYpNiNJJXpldGFHRiRGMSomRihGMS0mRi02I0YwRjJGMUYpLSZGLTYjLCZGMEYxRjFGMTYjSSJ5R0YkRjFGMQ==">KiYpSSJoRzYiIiIjISIiLCgtJkkidUdGJTYjLCZJIm1HRiUiIiJGL0YnNiNJJXpldGFHRiVGLyomRiZGLy0mRis2I0YuRjBGL0YnLSZGKzYjLCZGLkYvRi9GLzYjSSJ5R0YlRi9GLw==</Equation></Text-field>
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</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=subs(diff(u(x,y),x)=subs(m=0,fd1),u(x,y)=u[0](y),x=0,bc1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLSZJInVHRiQ2IyIiITYjSSJ5R0Yk">LSZJInVHNiI2IyIiITYjSSJ5R0Yl</Equation></Text-field>
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<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=subs(diff(u(x,y),x)=subs(m=N+1,bd1),u(x,y)=u[N+1](y),x=1,bc2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLSZJInVHRiQ2IywmSSJOR0YkIiIiRitGKzYjSSJ5R0Yk">LSZJInVHNiI2IywmSSJOR0YlIiIiRilGKTYjSSJ5R0Yl</Equation></Text-field>
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<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=10;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTkc2IiIjNQ==">IiM1</Equation></Text-field>
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<Group labelreference="L70" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
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<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[0]:=bc1; </Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiEtJkkidUdGJUYmNiNJInlHRiU=">LSZJInVHNiI2IyIiITYjSSJ5R0Yl</Equation></Text-field>
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<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[N+1]:=bc2; </Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzYtJkkidUdGJUYmNiNJInlHRiU=">LSZJInVHNiI2IyIjNjYjSSJ5R0Yl</Equation></Text-field>
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<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](y),y$2)=expand(subs(diff(u(x,y),x$2)=subs(m=i,cd2),diff(u(x,y),x)= ubs(m=i,cd1),diff(u(x,y),y)=u[N+1+i](y),u(x,y)=u[i](y),x=i*h,rhs(ge)));od;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvIiIhLCwtJkkidUdGJTYjIiM3NiNJInlHRiVGJyomIiRAIkYnLSZGLTYjRik2I0klemV0YUdGJUYnISIiKiYiJFUjRictJkYtRiZGN0YnRicqJkYzRictJkYtNiMiIiNGMEYnRjkqJiIjNkYnLUkkdWJzR0YlNiQvSSJtR0YlRicsJiomI0ZERkJGJy0mRi02IywmRklGJ0YnRidGMEYnRicqJkZMRictJkYtNiMsJkZJRidGJ0Y5RjdGJ0Y5RidGOQ==">LyIiISwsLSZJInVHNiI2IyIjNzYjSSJ5R0YoIiIiKiYiJEAiRi0tJkYnNiNGIzYjSSV6ZXRhR0YoRi0hIiIqJiIkVSNGLS0mRic2I0YtRjNGLUYtKiZGL0YtLSZGJzYjIiIjRitGLUY1KiYiIzZGLS1JJHVic0dGKDYkL0kibUdGKEYtLCYqJiNGQUY/Ri0tJkYnNiMsJkZGRi1GLUYtRitGLUYtKiZGSUYtLSZGJzYjLCZGRkYtRi1GNUYzRi1GNUYtRjU=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvIiIhLCwtJkkidUdGJTYjIiM4NiNJInlHRiUiIiIqJiIkQCJGMi0mRi02I0YyNiNJJXpldGFHRiVGMiEiIiomIiRVI0YyLSZGLUYmRjhGMkYyKiZGNEYyLSZGLTYjIiIkRjBGMkY6KiYjIiM2RidGMi1JJHVic0dGJTYkL0kibUdGJUYnLCYqJkZFRjItJkYtNiMsJkZLRjJGMkYyRjBGMkYyKiZGRUYyLSZGLTYjLCZGS0YyRjJGOkY4RjJGOkYyRjo=">LyIiISwsLSZJInVHNiI2IyIjODYjSSJ5R0YoIiIiKiYiJEAiRi0tJkYnNiNGLTYjSSV6ZXRhR0YoRi0hIiIqJiIkVSNGLS0mRic2IyIiI0YzRi1GLSomRi9GLS0mRic2IyIiJEYrRi1GNSomIyIjNkY7Ri0tSSR1YnNHRig2JC9JIm1HRihGOywmKiZGQkYtLSZGJzYjLCZGSEYtRi1GLUYrRi1GLSomRkJGLS0mRic2IywmRkhGLUYtRjVGM0YtRjVGLUY1</Equation></Text-field>
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<Output>
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</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiUvIiIhLCwtJkkidUdGJTYjIiM6NiNJInlHRiUiIiIqJiIkQCJGMi0mRi02IyIiJDYjSSV6ZXRhR0YlRjIhIiIqJiIkVSNGMi0mRi1GJkY5RjJGMiomRjRGMi0mRi02IyIiJkYwRjJGOyomIyIjNkYnRjItSSR1YnNHRiU2JC9JIm1HRiVGJywmKiYjRkciIiNGMi0mRi02IywmRkxGMkYyRjJGMEYyRjIqJkZPRjItJkYtNiMsJkZMRjJGMkY7RjlGMkY7RjJGOw==">LyIiISwsLSZJInVHNiI2IyIjOjYjSSJ5R0YoIiIiKiYiJEAiRi0tJkYnNiMiIiQ2I0klemV0YUdGKEYtISIiKiYiJFUjRi0tJkYnNiMiIiVGNEYtRi0qJkYvRi0tJkYnNiMiIiZGK0YtRjYqJiMiIzZGPEYtLUkkdWJzR0YoNiQvSSJtR0YoRjwsJiomI0ZEIiIjRi0tJkYnNiMsJkZJRi1GLUYtRitGLUYtKiZGTEYtLSZGJzYjLCZGSUYtRi1GNkY0Ri1GNkYtRjY=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiYvIiIhLCwtJkkidUdGJTYjIiM7NiNJInlHRiUiIiIqJiIkQCJGMi0mRi02IyIiJTYjSSV6ZXRhR0YlRjIhIiIqJiIkVSNGMi0mRi1GJkY5RjJGMiomRjRGMi0mRi02IyIiJ0YwRjJGOyomIyIjNkYnRjItSSR1YnNHRiU2JC9JIm1HRiVGJywmKiYjRkciIiNGMi0mRi02IywmRkxGMkYyRjJGMEYyRjIqJkZPRjItJkYtNiMsJkZMRjJGMkY7RjlGMkY7RjJGOw==">LyIiISwsLSZJInVHNiI2IyIjOzYjSSJ5R0YoIiIiKiYiJEAiRi0tJkYnNiMiIiU2I0klemV0YUdGKEYtISIiKiYiJFUjRi0tJkYnNiMiIiZGNEYtRi0qJkYvRi0tJkYnNiMiIidGK0YtRjYqJiMiIzZGPEYtLUkkdWJzR0YoNiQvSSJtR0YoRjwsJiomI0ZEIiIjRi0tJkYnNiMsJkZJRi1GLUYtRitGLUYtKiZGTEYtLSZGJzYjLCZGSUYtRi1GNkY0Ri1GNkYtRjY=</Equation></Text-field>
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<Output>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIigvIiIhLCwtJkkidUdGJTYjIiM9NiNJInlHRiUiIiIqJiIkQCJGMi0mRi02IyIiJzYjSSV6ZXRhR0YlRjIhIiIqJiIkVSNGMi0mRi1GJkY5RjJGMiomRjRGMi0mRi02IyIiKUYwRjJGOyomIyIjNkYnRjItSSR1YnNHRiU2JC9JIm1HRiVGJywmKiYjRkciIiNGMi0mRi02IywmRkxGMkYyRjJGMEYyRjIqJkZPRjItJkYtNiMsJkZMRjJGMkY7RjlGMkY7RjJGOw==">LyIiISwsLSZJInVHNiI2IyIjPTYjSSJ5R0YoIiIiKiYiJEAiRi0tJkYnNiMiIic2I0klemV0YUdGKEYtISIiKiYiJFUjRi0tJkYnNiMiIihGNEYtRi0qJkYvRi0tJkYnNiMiIilGK0YtRjYqJiMiIzZGPEYtLUkkdWJzR0YoNiQvSSJtR0YoRjwsJiomI0ZEIiIjRi0tJkYnNiMsJkZJRi1GLUYtRitGLUYtKiZGTEYtLSZGJzYjLCZGSUYtRi1GNkY0Ri1GNkYtRjY=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIikvIiIhLCwtJkkidUdGJTYjIiM+NiNJInlHRiUiIiIqJiIkQCJGMi0mRi02IyIiKDYjSSV6ZXRhR0YlRjIhIiIqJiIkVSNGMi0mRi1GJkY5RjJGMiomRjRGMi0mRi02IyIiKkYwRjJGOyomIyIjNkYnRjItSSR1YnNHRiU2JC9JIm1HRiVGJywmKiYjRkciIiNGMi0mRi02IywmRkxGMkYyRjJGMEYyRjIqJkZPRjItJkYtNiMsJkZMRjJGMkY7RjlGMkY7RjJGOw==">LyIiISwsLSZJInVHNiI2IyIjPjYjSSJ5R0YoIiIiKiYiJEAiRi0tJkYnNiMiIig2I0klemV0YUdGKEYtISIiKiYiJFUjRi0tJkYnNiMiIilGNEYtRi0qJkYvRi0tJkYnNiMiIipGK0YtRjYqJiMiIzZGPEYtLUkkdWJzR0YoNiQvSSJtR0YoRjwsJiomI0ZEIiIjRi0tJkYnNiMsJkZJRi1GLUYtRitGLUYtKiZGTEYtLSZGJzYjLCZGSUYtRi1GNkY0Ri1GNkYtRjY=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiovIiIhLCwtJkkidUdGJTYjIiM/NiNJInlHRiUiIiIqJiIkQCJGMi0mRi02IyIiKTYjSSV6ZXRhR0YlRjIhIiIqJiIkVSNGMi0mRi1GJkY5RjJGMiomRjRGMi0mRi02IyIjNUYwRjJGOyomIyIjNkYnRjItSSR1YnNHRiU2JC9JIm1HRiVGJywmKiYjRkciIiNGMi0mRi02IywmRkxGMkYyRjJGMEYyRjIqJkZPRjItJkYtNiMsJkZMRjJGMkY7RjlGMkY7RjJGOw==">LyIiISwsLSZJInVHNiI2IyIjPzYjSSJ5R0YoIiIiKiYiJEAiRi0tJkYnNiMiIik2I0klemV0YUdGKEYtISIiKiYiJFUjRi0tJkYnNiMiIipGNEYtRi0qJkYvRi0tJkYnNiMiIzVGK0YtRjYqJiMiIzZGPEYtLUkkdWJzR0YoNiQvSSJtR0YoRjwsJiomI0ZEIiIjRi0tJkYnNiMsJkZJRi1GLUYtRitGLUYtKiZGTEYtLSZGJzYjLCZGSUYtRi1GNkY0Ri1GNkYtRjY=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzUvIiIhLCwtJkkidUdGJTYjIiNANiNJInlHRiUiIiIqJiIkQCJGMi0mRi02IyIiKjYjSSV6ZXRhR0YlRjIhIiIqJiIkVSNGMi0mRi1GJkY5RjJGMiomRjRGMi0mRi02IyIjNkYwRjJGOyomI0ZERidGMi1JJHVic0dGJTYkL0kibUdGJUYnLCYqJiNGRCIiI0YyLSZGLTYjLCZGS0YyRjJGMkYwRjJGMiomRk5GMi0mRi02IywmRktGMkYyRjtGOUYyRjtGMkY7">LyIiISwsLSZJInVHNiI2IyIjQDYjSSJ5R0YoIiIiKiYiJEAiRi0tJkYnNiMiIio2I0klemV0YUdGKEYtISIiKiYiJFUjRi0tJkYnNiMiIzVGNEYtRi0qJkYvRi0tJkYnNiMiIzZGK0YtRjYqJiNGQUY8Ri0tSSR1YnNHRig2JC9JIm1HRihGPCwmKiYjRkEiIiNGLS0mRic2IywmRkhGLUYtRi1GK0YtRi0qJkZLRi0tJkYnNiMsJkZIRi1GLUY2RjRGLUY2Ri1GNg==</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u[0](y):=(solve(eq[0],u[0](y)));</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiE2I0kieUdGJkYo">IiIh</Equation></Text-field>
</Output>
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<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u[N+1](y):=solve(eq[N+1],u[N+1](y));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIzY2I0kieUdGJiIiIQ==">IiIh</Equation></Text-field>
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<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>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiaEc2IiMiIiIiIzY=">IyIiIiIjNg==</Equation></Text-field>
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<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N do eq[i]:=eval(eq[i]);od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kieUdGJS1JIiRHRis2JEYxIiIjLCotJkYvNiMiIzdGMEYnKiYjIiRAIkY1RictJkYvNiMiIiE2I0klemV0YUdGJUYnISIiKiYiJFUjRictRi5GQkYnRicqJiMiJGokRjVGJy0mRi82I0Y1RjBGJ0ZE">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC0mSSJ1RzYiNiMiIiI2I0kieUdGLEYwRjAsKi0mRis2IyIjN0YvRi4qJiMiJEAiIiIjRi4tJkYrNiMiIiE2I0klemV0YUdGLEYuISIiKiYiJFUjRi4tRipGPkYuRi4qJiMiJGokRjlGLi0mRis2I0Y5Ri9GLkZA</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kieUdGJS1JIiRHRis2JEYxRicsKi0mRi82IyIjOEYwIiIiKiYjIiRqJCIiJUY6LSZGLzYjRjo2I0klemV0YUdGJUY6ISIiKiYiJFUjRjotRi5GQkY6RjoqJiMiJDAnRj5GOi0mRi82IyIiJEYwRjpGRA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC0mSSJ1RzYiNiMiIiM2I0kieUdGLEYwRjAsKi0mRis2IyIjOEYvIiIiKiYjIiRqJCIiJUY2LSZGKzYjRjY2I0klemV0YUdGLEY2ISIiKiYiJFUjRjYtRipGPkY2RjYqJiMiJDAnRjpGNi0mRis2IyIiJEYvRjZGQA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kieUdGJS1JIiRHRis2JEYxIiIjLCotJkYvNiMiIzlGMCIiIiomIyIkMCciIidGOy0mRi82I0Y1NiNJJXpldGFHRiVGOyEiIiomIiRVI0Y7LUYuRkNGO0Y7KiYjIiRaKUY/RjstJkYvNiMiIiVGMEY7RkU=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC0mSSJ1RzYiNiMiIiQ2I0kieUdGLEYwRjAsKi0mRis2IyIjOUYvIiIiKiYjIiQwJyIiJ0Y2LSZGKzYjIiIjNiNJJXpldGFHRixGNiEiIiomIiRVI0Y2LUYqRj9GNkY2KiYjIiRaKUY6RjYtJkYrNiMiIiVGL0Y2RkE=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kieUdGJS1JIiRHRis2JEYxIiIjLCotJkYvNiMiIzpGMCIiIiomIyIkWikiIilGOy0mRi82IyIiJDYjSSV6ZXRhR0YlRjshIiIqJiIkVSNGOy1GLkZERjtGOyomIyIlKjMiRj9GOy0mRi82IyIiJkYwRjtGRg==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC0mSSJ1RzYiNiMiIiU2I0kieUdGLEYwRjAsKi0mRis2IyIjOkYvIiIiKiYjIiRaKSIiKUY2LSZGKzYjIiIkNiNJJXpldGFHRixGNiEiIiomIiRVI0Y2LUYqRj9GNkY2KiYjIiUqMyJGOkY2LSZGKzYjIiImRi9GNkZB</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiYvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kieUdGJS1JIiRHRis2JEYxIiIjLCotJkYvNiMiIztGMCIiIiomIyIlKjMiIiM1RjstJkYvNiMiIiU2I0klemV0YUdGJUY7ISIiKiYiJFUjRjstRi5GREY7RjsqJiMiJUo4Rj9GOy0mRi82IyIiJ0YwRjtGRg==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC0mSSJ1RzYiNiMiIiY2I0kieUdGLEYwRjAsKi0mRis2IyIjO0YvIiIiKiYjIiUqMyIiIzVGNi0mRis2IyIiJTYjSSV6ZXRhR0YsRjYhIiIqJiIkVSNGNi1GKkY/RjZGNiomIyIlSjhGOkY2LSZGKzYjIiInRi9GNkZB</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIicvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kieUdGJS1JIiRHRis2JEYxIiIjLCotJkYvNiMiIzxGMCIiIiomIyIlSjgiIzdGOy0mRi82IyIiJjYjSSV6ZXRhR0YlRjshIiIqJiIkVSNGOy1GLkZERjtGOyomIyIldDpGP0Y7LSZGLzYjIiIoRjBGO0ZG">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC0mSSJ1RzYiNiMiIic2I0kieUdGLEYwRjAsKi0mRis2IyIjPEYvIiIiKiYjIiVKOCIjN0Y2LSZGKzYjIiImNiNJJXpldGFHRixGNiEiIiomIiRVI0Y2LUYqRj9GNkY2KiYjIiV0OkY6RjYtJkYrNiMiIihGL0Y2RkE=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIigvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kieUdGJS1JIiRHRis2JEYxIiIjLCotJkYvNiMiIz1GMCIiIiomIyIldDoiIzlGOy0mRi82IyIiJzYjSSV6ZXRhR0YlRjshIiIqJiIkVSNGOy1GLkZERjtGOyomIyIlOj1GP0Y7LSZGLzYjIiIpRjBGO0ZG">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC0mSSJ1RzYiNiMiIig2I0kieUdGLEYwRjAsKi0mRis2IyIjPUYvIiIiKiYjIiV0OiIjOUY2LSZGKzYjIiInNiNJJXpldGFHRixGNiEiIiomIiRVI0Y2LUYqRj9GNkY2KiYjIiU6PUY6RjYtJkYrNiMiIilGL0Y2RkE=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIikvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kieUdGJS1JIiRHRis2JEYxIiIjLCotJkYvNiMiIz5GMCIiIiomIyIlOj0iIztGOy0mRi82IyIiKDYjSSV6ZXRhR0YlRjshIiIqJiIkVSNGOy1GLkZERjtGOyomIyIlZD9GP0Y7LSZGLzYjIiIqRjBGO0ZG">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC0mSSJ1RzYiNiMiIik2I0kieUdGLEYwRjAsKi0mRis2IyIjPkYvIiIiKiYjIiU6PSIjO0Y2LSZGKzYjIiIoNiNJJXpldGFHRixGNiEiIiomIiRVI0Y2LUYqRj9GNkY2KiYjIiVkP0Y6RjYtJkYrNiMiIipGL0Y2RkE=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiovLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kieUdGJS1JIiRHRis2JEYxIiIjLCotJkYvNiMiIz9GMCIiIiomIyIlZD8iIz1GOy0mRi82IyIiKTYjSSV6ZXRhR0YlRjshIiIqJiIkVSNGOy1GLkZERjtGOyomIyIlKkgjRj9GOy0mRi82IyIjNUYwRjtGRg==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC0mSSJ1RzYiNiMiIio2I0kieUdGLEYwRjAsKi0mRis2IyIjP0YvIiIiKiYjIiVkPyIjPUY2LSZGKzYjIiIpNiNJJXpldGFHRixGNiEiIiomIiRVI0Y2LUYqRj9GNkY2KiYjIiUqSCNGOkY2LSZGKzYjIiM1Ri9GNkZB</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kieUdGJS1JIiRHRis2JEYxIiIjLCgtJkYvNiMiI0BGMCIiIiomIyIlKkgjIiM/RjstJkYvNiMiIio2I0klemV0YUdGJUY7ISIiKiYiJFUjRjstRi5GREY7Rjs=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC0mSSJ1RzYiNiMiIzU2I0kieUdGLEYwRjAsKC0mRis2IyIjQEYvIiIiKiYjIiUqSCMiIz9GNi0mRis2IyIiKjYjSSV6ZXRhR0YsRjYhIiIqJiIkVSNGNi1GKkY/RjZGNg==</Equation></Text-field>
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<Group labelreference="L74" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Boundary condtions in y are convered to index form and use with the governing equations in the interior node points to obtain a numerical solution.</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">BC3:=seq(subs(diff(u(x,y),y)=D(u[i])(0),u(x,y)=u[i](0),x=i*h,bc3,i=1..N)</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"></Text-field>
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<Output>
<Text-field style="Warning" layout="Warning">Warning, premature end of input, use &lt;Shift&gt; + &lt;Enter&gt; to avoid this message.</Text-field>
</Output>
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<Group labelreference="L29" 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>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">h:=eval(1/(N+1));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiaEc2IiMiIiIiIzY=">IyIiIiIjNg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=evalm(exponential(A,zeta)):</Text-field>
</Input>
<Output>
<Text-field style="Error" layout="Error">Error, (in linalg:-matfunc) input must be a matrix</Text-field>
</Output>
</Group>
<Group labelreference="L35" 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="L36" 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="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat2:=evalm(mat1&amp;*b2):</Text-field>
</Input>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat2:=map(expand,mat2):</Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat3:=map(int,mat2,zeta1=0..zeta):</Text-field>
</Input>
<Output>
<Text-field style="Error" layout="Error">Error, (in int) wrong number (or type) of arguments</Text-field>
</Output>
</Group>
<Group labelreference="L40" 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="PkkjWTBHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIz87RipGKjci">PTYiNiQ7IiIiIiM/O0YmRiZFXFtsIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L41" 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="L42" 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="L43" 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="LUknbWF0cml4RzYiNiM3NjcjJkkicEdGJDYjIiIiNyMmRik2IyIiIzcjJkYpNiMiIiQ3IyZGKTYjIiIlNyMmRik2IyIiJjcjJkYpNiMiIic3IyZGKTYjIiIoNyMmRik2IyIiKTcjJkYpNiMiIio3IyZGKTYjIiM1NyMmSSJjR0YkRio3IyZGUkYuNyMmRlJGMjcjJkZSRjY3IyZGUkY6NyMmRlJGPjcjJkZSRkI3IyZGUkZGNyMmRlJGSjcjJkZSRk4=">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=evalm(mat&amp;*Y0+mat3):</Text-field>
</Input>
</Group>
<Group labelreference="L45" 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="L46" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol1:=map(eval,evalm(subs(zeta=epsilon*H/h,evalm(Y)))):</Text-field>
</Input>
</Group>
<Group labelreference="L47" 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="PiZJI0VxRzYiNiMiIiIvJkkicEdGJUYmIiIh">LyZJInBHNiI2IyIiIiIiIQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiMvJkkicEdGJUYmIiIh">LyZJInBHNiI2IyIiIyIiIQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiQvJkkicEdGJUYmIiIh">LyZJInBHNiI2IyIiJCIiIQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiUvJkkicEdGJUYmIiIh">LyZJInBHNiI2IyIiJSIiIQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiYvJkkicEdGJUYmIiIh">LyZJInBHNiI2IyIiJiIiIQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIicvJkkicEdGJUYmIiIh">LyZJInBHNiI2IyIiJyIiIQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIigvJkkicEdGJUYmIiIh">LyZJInBHNiI2IyIiKCIiIQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIikvJkkicEdGJUYmIiIh">LyZJInBHNiI2IyIiKSIiIQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiovJkkicEdGJUYmIiIh">LyZJInBHNiI2IyIiKiIiIQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzUvJkkicEdGJUYmIiIh">LyZJInBHNiI2IyIjNSIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L48" 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="PiZJI0VxRzYiNiMiIzYvLCYmLCYtSSMmKkdGJTYkSSRtYXRHRiUtSSdtYXRyaXhHRiU2Izc2NyMmSSJwR0YlNiMiIiI3IyZGNjYjIiIjNyMmRjY2IyIiJDcjJkY2NiMiIiU3IyZGNjYjIiImNyMmRjY2IyIiJzcjJkY2NiMiIig3IyZGNjYjIiIpNyMmRjY2IyIiKjcjJkY2NiMiIzU3IyZJImNHRiVGNzcjJkZpbkY7NyMmRmluRj83IyZGaW5GQzcjJkZpbkZHNyMmRmluRks3IyZGaW5GTzcjJkZpbkZTNyMmRmluRlc3IyZGaW5GZW5GOEklbWF0M0dGJUY4NiRGOEY4RjgkRjgiIiEhIiIkRl9wRl9w">[encoded data, 16416 characters]</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzcvLCYmLCYtSSMmKkdGJTYkSSRtYXRHRiUtSSdtYXRyaXhHRiU2Izc2NyMmSSJwR0YlNiMiIiI3IyZGNjYjIiIjNyMmRjY2IyIiJDcjJkY2NiMiIiU3IyZGNjYjIiImNyMmRjY2IyIiJzcjJkY2NiMiIig3IyZGNjYjIiIpNyMmRjY2IyIiKjcjJkY2NiMiIzU3IyZJImNHRiVGNzcjJkZpbkY7NyMmRmluRj83IyZGaW5GQzcjJkZpbkZHNyMmRmluRks3IyZGaW5GTzcjJkZpbkZTNyMmRmluRlc3IyZGaW5GZW5GOEklbWF0M0dGJUY4NiRGPEY4RjgkRjgiIiEhIiIkRl9wRl9w">[encoded data, 16416 characters]</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzgvLCYmLCYtSSMmKkdGJTYkSSRtYXRHRiUtSSdtYXRyaXhHRiU2Izc2NyMmSSJwR0YlNiMiIiI3IyZGNjYjIiIjNyMmRjY2IyIiJDcjJkY2NiMiIiU3IyZGNjYjIiImNyMmRjY2IyIiJzcjJkY2NiMiIig3IyZGNjYjIiIpNyMmRjY2IyIiKjcjJkY2NiMiIzU3IyZJImNHRiVGNzcjJkZpbkY7NyMmRmluRj83IyZGaW5GQzcjJkZpbkZHNyMmRmluRks3IyZGaW5GTzcjJkZpbkZTNyMmRmluRlc3IyZGaW5GZW5GOEklbWF0M0dGJUY4NiRGQEY4RjgkRjgiIiEhIiIkRl9wRl9w">[encoded data, 16416 characters]</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzkvLCYmLCYtSSMmKkdGJTYkSSRtYXRHRiUtSSdtYXRyaXhHRiU2Izc2NyMmSSJwR0YlNiMiIiI3IyZGNjYjIiIjNyMmRjY2IyIiJDcjJkY2NiMiIiU3IyZGNjYjIiImNyMmRjY2IyIiJzcjJkY2NiMiIig3IyZGNjYjIiIpNyMmRjY2IyIiKjcjJkY2NiMiIzU3IyZJImNHRiVGNzcjJkZpbkY7NyMmRmluRj83IyZGaW5GQzcjJkZpbkZHNyMmRmluRks3IyZGaW5GTzcjJkZpbkZTNyMmRmluRlc3IyZGaW5GZW5GOEklbWF0M0dGJUY4NiRGREY4RjgkRjgiIiEhIiIkRl9wRl9w">[encoded data, 16416 characters]</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzovLCYmLCYtSSMmKkdGJTYkSSRtYXRHRiUtSSdtYXRyaXhHRiU2Izc2NyMmSSJwR0YlNiMiIiI3IyZGNjYjIiIjNyMmRjY2IyIiJDcjJkY2NiMiIiU3IyZGNjYjIiImNyMmRjY2IyIiJzcjJkY2NiMiIig3IyZGNjYjIiIpNyMmRjY2IyIiKjcjJkY2NiMiIzU3IyZJImNHRiVGNzcjJkZpbkY7NyMmRmluRj83IyZGaW5GQzcjJkZpbkZHNyMmRmluRks3IyZGaW5GTzcjJkZpbkZTNyMmRmluRlc3IyZGaW5GZW5GOEklbWF0M0dGJUY4NiRGSEY4RjgkRjgiIiEhIiIkRl9wRl9w">[encoded data, 16416 characters]</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzsvLCYmLCYtSSMmKkdGJTYkSSRtYXRHRiUtSSdtYXRyaXhHRiU2Izc2NyMmSSJwR0YlNiMiIiI3IyZGNjYjIiIjNyMmRjY2IyIiJDcjJkY2NiMiIiU3IyZGNjYjIiImNyMmRjY2IyIiJzcjJkY2NiMiIig3IyZGNjYjIiIpNyMmRjY2IyIiKjcjJkY2NiMiIzU3IyZJImNHRiVGNzcjJkZpbkY7NyMmRmluRj83IyZGaW5GQzcjJkZpbkZHNyMmRmluRks3IyZGaW5GTzcjJkZpbkZTNyMmRmluRlc3IyZGaW5GZW5GOEklbWF0M0dGJUY4NiRGTEY4RjgkRjgiIiEhIiIkRl9wRl9w">[encoded data, 16416 characters]</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzwvLCYmLCYtSSMmKkdGJTYkSSRtYXRHRiUtSSdtYXRyaXhHRiU2Izc2NyMmSSJwR0YlNiMiIiI3IyZGNjYjIiIjNyMmRjY2IyIiJDcjJkY2NiMiIiU3IyZGNjYjIiImNyMmRjY2IyIiJzcjJkY2NiMiIig3IyZGNjYjIiIpNyMmRjY2IyIiKjcjJkY2NiMiIzU3IyZJImNHRiVGNzcjJkZpbkY7NyMmRmluRj83IyZGaW5GQzcjJkZpbkZHNyMmRmluRks3IyZGaW5GTzcjJkZpbkZTNyMmRmluRlc3IyZGaW5GZW5GOEklbWF0M0dGJUY4NiRGUEY4RjgkRjgiIiEhIiIkRl9wRl9w">[encoded data, 16416 characters]</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIz0vLCYmLCYtSSMmKkdGJTYkSSRtYXRHRiUtSSdtYXRyaXhHRiU2Izc2NyMmSSJwR0YlNiMiIiI3IyZGNjYjIiIjNyMmRjY2IyIiJDcjJkY2NiMiIiU3IyZGNjYjIiImNyMmRjY2IyIiJzcjJkY2NiMiIig3IyZGNjYjIiIpNyMmRjY2IyIiKjcjJkY2NiMiIzU3IyZJImNHRiVGNzcjJkZpbkY7NyMmRmluRj83IyZGaW5GQzcjJkZpbkZHNyMmRmluRks3IyZGaW5GTzcjJkZpbkZTNyMmRmluRlc3IyZGaW5GZW5GOEklbWF0M0dGJUY4NiRGVEY4RjgkRjgiIiEhIiIkRl9wRl9w">[encoded data, 16416 characters]</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIz4vLCYmLCYtSSMmKkdGJTYkSSRtYXRHRiUtSSdtYXRyaXhHRiU2Izc2NyMmSSJwR0YlNiMiIiI3IyZGNjYjIiIjNyMmRjY2IyIiJDcjJkY2NiMiIiU3IyZGNjYjIiImNyMmRjY2IyIiJzcjJkY2NiMiIig3IyZGNjYjIiIpNyMmRjY2IyIiKjcjJkY2NiMiIzU3IyZJImNHRiVGNzcjJkZpbkY7NyMmRmluRj83IyZGaW5GQzcjJkZpbkZHNyMmRmluRks3IyZGaW5GTzcjJkZpbkZTNyMmRmluRlc3IyZGaW5GZW5GOEklbWF0M0dGJUY4NiRGWEY4RjgkRjgiIiEhIiIkRl9wRl9w">[encoded data, 16416 characters]</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIz8vLCYmLCYtSSMmKkdGJTYkSSRtYXRHRiUtSSdtYXRyaXhHRiU2Izc2NyMmSSJwR0YlNiMiIiI3IyZGNjYjIiIjNyMmRjY2IyIiJDcjJkY2NiMiIiU3IyZGNjYjIiImNyMmRjY2IyIiJzcjJkY2NiMiIig3IyZGNjYjIiIpNyMmRjY2IyIiKjcjJkY2NiMiIzU3IyZJImNHRiVGNzcjJkZpbkY7NyMmRmluRj83IyZGaW5GQzcjJkZpbkZHNyMmRmluRks3IyZGaW5GTzcjJkZpbkZTNyMmRmluRlc3IyZGaW5GZW5GOEklbWF0M0dGJUY4NiRGZm5GOEY4JEY4IiIhISIiJEZfcEZfcA==">LywmJiwmLUkjJipHNiI2JEkkbWF0R0YoPUYoNiQ7IiIiIiM/O0YuRi5FXFtsNTYkIiIkRi4mSSJwR0YoNiNGMzYkIiM5Ri4mSSJjR0YoNiMiIiU2JCIiKUYuJkY1NiNGPjYkIiM9Ri4mRjpGQDYkIiM8Ri4mRjo2IyIiKDYkIiImRi4mRjU2I0ZKNiQiIzdGLiZGOjYjIiIjNiRGLkYuJkY1NiNGLjYkIiM2Ri4mRjpGVDYkIiInRi4mRjU2I0ZZNiRGPEYuJkY1Rjs2JCIjO0YuJkY6RmVuNiQiIipGLiZGNTYjRlxvNiQiIz5GLiZGOkZebzYkIiM4Ri4mRjpGNjYkRlFGLiZGNUZQNiQiIzVGLiZGNTYjRmhvNiQiIzpGLiZGOkZMNiRGL0YuJkY6RmpvNiRGSEYuJkY1RkdGLkklbWF0M0dGKEYuRmdvRi4kRi4iIiEhIiIkRmRwRmRw</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L49" 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="PkklY3NvbEc2IkYk">PiUlY3NvbEc2Ig==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">assign(csol);</Text-field>
</Input>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=map(eval,Y):</Text-field>
</Input>
</Group>
<Group labelreference="L52" 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="L53" 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="L54" 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>
</Group>
<Group labelreference="L55" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 do p[i]:=plot(u[i](y),y=0..H,thickness=3);od:</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
</Group>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({seq(p[i],i=0..N+1)},axes=boxed,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">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">M:=20;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTUc2IiIjPw==">IiM/</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L58" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T1:=[seq(evalf(i*H/M),i=0..M)]:</Text-field>
</Input>
</Group>
<Group labelreference="L59" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P[1]:=plot([seq([h*i,0.],i=0..N+1)],style=line,thickness=3,axes=boxed,view=[0..1,0..1.1]):</Text-field>
</Input>
</Group>
<Group labelreference="L60" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for j from 2 to M+1 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>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
</Group>
<Group labelreference="L61" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({seq(P[i],i=1..M+1)},labels=[x,u]);</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">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L62" 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="L63" 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="PkkjUFBHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIzc7RioiI0k3Ig==">PTYiNiQ7IiIiIiM3O0YmIiNJRVxbbCE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L64" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N+2 do for j from 1 to Ny do PP[i,j]:=evalf(subs(y=(j-1)*H/(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">PP[N+2,1]:=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI1BQRzYiNiQiIzciIiIiIiE=">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L66" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plotdata := [seq([ seq([(i-1)/(N+1),(j-1)*H/(Ny-1),PP[i,j]], i=1..N+2)], j=1..Ny)]:</Text-field>
</Input>
</Group>
<Group labelreference="L67" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">surfdata( plotdata, axes=boxed, labels=[x,y,u],orientation=[-150,45] );</Text-field>
</Input>
<Output>
<Text-field style="Error" layout="Error">Error, (in plots/surfdata) incorrect format for input points</Text-field>
</Output>
</Group>
<Group labelreference="L68" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>