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<Input>
<Text-field style="Text" layout="Normal">Example 5.6 Semianalytical Method for the Graetz Problem</Text-field>
</Input>
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<Group labelreference="L86" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Equation (5.1.30) is solved in Maple using the Maple program developed for example 5.2 by making very few changes:</Text-field>
</Input>
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<Group labelreference="L77" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart;</Text-field>
</Input>
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<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">ge:=diff(u(x,t),t)=1/(1-x^2)*diff(u(x,t),x$2)+1/(1-x^2)/x*diff(u(x,t),x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZ2VHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkidEdGJEYuLCYqJiwmIiIiRjIqJClGLSIiI0YyISIiRjYtRic2JEYqLUkiJEdGKDYkRi1GNUYyRjIqKEYxRjZGLUY2LUYnNiRGKkYtRjJGMg==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLCwmKiYsJiIiIkYwKiRGKyIiIyEiIkYzLUYkNiQtRiQ2JEYnRitGK0YwRjAqKEYvRjNGK0YzRjZGMEYw</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=diff(u(x,t),x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkidEdGJEYs">LUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHNiI2JEkieEdGKEkidEdGKEYq</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,t)-1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLCYtSSJ1R0YkNiRJInhHRiRJInRHRiQiIiJGKyEiIg==">LCYtSSJ1RzYiNiRJInhHRiVJInRHRiUiIiIhIiJGKQ==</Equation></Text-field>
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<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IC:=u(x,0)=0;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSUNHNiIvLUkidUdGJDYkSSJ4R0YkIiIhRio=">Ly1JInVHNiI2JEkieEdGJSIiIUYo</Equation></Text-field>
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<Group labelreference="L8" 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="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">L:=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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</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxf:=1/2*(-u[2](t)-3*u[0](t)+4*u[1](t))/h:</Text-field>
</Input>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxb:=1/2*(u[N-1](t)+3*u[N+1](t)-4*u[N](t))/h:</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydx:=1/2/h*(u[m+1](t)-u[m-1](t)):</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">d2ydx2:=1/h^2*(u[m-1](t)-2*u[m](t)+u[m+1](t)):</Text-field>
</Input>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=subs(diff(u(x,t),x)=dydxf,u(x,t)=u[0](t),x=0,bc1):</Text-field>
</Input>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=subs(diff(u(x,t),x)=dydxb,u(x,t)=u[N+1](t),x=1,bc2):</Text-field>
</Input>
</Group>
<Group labelreference="L16" 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="PiZJI2VxRzYiNiMiIiEsJCooIyIiIiIiI0YrLCgtJkkidUdGJTYjRiw2I0kidEdGJSEiIiomIiIkRistJkYwRiZGMkYrRjQqJiIiJUYrLSZGMDYjRitGMkYrRitGK0kiaEdGJUY0Ris=">LCQqJiwoLSZJInVHNiI2IyIiIzYjSSJ0R0YoISIiLSZGJzYjIiIhRishIiQtJkYnNiMiIiJGKyIiJUY2SSJoR0YoRi0jRjZGKg==</Equation></Text-field>
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<Group labelreference="L17" 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="PiZJI2VxRzYiNiMiIzYsJi0mSSJ1R0YlRiY2I0kidEdGJSIiIkYuISIi">LCYtJkkidUc2IjYjIiM2NiNJInRHRiYiIiIhIiJGKw==</Equation></Text-field>
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</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N do eq[i]:=diff(u[i](t),t)= subs(diff(u(x,t),x$2) = subs(m=i,d2ydx2),diff(u(x,t),x) = subs(m=i,dydx),u(x,t)=u[i](t),x=i*h,rhs(ge));od;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmRidGJyokKUkiaEdGJSIiI0YnISIiRjlGNkY5LCgtJkYvNiMiIiFGMEYnKiZGOEYnRi1GJ0Y5LSZGLzYjRjhGMEYnRidGJyoqI0YnRjhGJ0Y0RjlGNkY5LCZGQEYnRjtGOUYnRic=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIiNiNJInRHRipGLiwmKigsJkYsRiwqJEkiaEdGKiIiIyEiIkY1RjMhIiMsKC0mRik2IyIiIUYtRixGJ0Y2LSZGKTYjRjRGLUYsRixGLCooRjFGNUYzRjYsJkY8RixGOEY1RiwjRixGNA==</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIiJUY1KUkiaEdGJUYnRjUhIiJGOkY4RjosKC0mRi82I0Y1RjBGNSomRidGNUYtRjVGOi0mRi82IyIiJEYwRjVGNUY1KiojRjVGN0Y1RjRGOkY4RjosJkZARjVGPEY6RjVGNQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIjNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRipGLCEiJSEiIkY0ISIjLCgtJkYpNiNGMkYtRjJGJ0Y3LSZGKTYjIiIkRi1GMkYyRjIqKEYxRjZGNEY3LCZGPEYyRjlGNkYyI0YyIiIl</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIiKkY1KUkiaEdGJSIiI0Y1ISIiRjtGOEY7LCgtJkYvNiNGOkYwRjUqJkY6RjVGLUY1RjstJkYvNiMiIiVGMEY1RjVGNSoqI0Y1IiInRjVGNEY7RjhGOywmRkFGNUY9RjtGNUY1">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIkNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhIiohIiJGNCEiIywoLSZGKTYjRjVGLUYyRidGOC0mRik2IyIiJUYtRjJGMkYyKihGMUY3RjRGOCwmRj1GMkY6RjdGMiNGMiIiJw==</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIjO0Y1KUkiaEdGJSIiI0Y1ISIiRjtGOEY7LCgtJkYvNiMiIiRGMEY1KiZGOkY1Ri1GNUY7LSZGLzYjIiImRjBGNUY1RjUqKiNGNSIiKUY1RjRGO0Y4RjssJkZCRjVGPUY7RjVGNQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIlNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhIzshIiJGNCEiIywoLSZGKTYjIiIkRi1GMkYnRjgtJkYpNiMiIiZGLUYyRjJGMiooRjFGN0Y0RjgsJkY+RjJGOkY3RjIjRjIiIik=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiYvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIjREY1KUkiaEdGJSIiI0Y1ISIiRjtGOEY7LCgtJkYvNiMiIiVGMEY1KiZGOkY1Ri1GNUY7LSZGLzYjIiInRjBGNUY1RjUqKiNGNSIjNUY1RjRGO0Y4RjssJkZCRjVGPUY7RjVGNQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiImNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhI0QhIiJGNCEiIywoLSZGKTYjIiIlRi1GMkYnRjgtJkYpNiMiIidGLUYyRjJGMiooRjFGN0Y0RjgsJkY+RjJGOkY3RjIjRjIiIzU=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIicvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIjT0Y1KUkiaEdGJSIiI0Y1ISIiRjtGOEY7LCgtJkYvNiMiIiZGMEY1KiZGOkY1Ri1GNUY7LSZGLzYjIiIoRjBGNUY1RjUqKiNGNSIjN0Y1RjRGO0Y4RjssJkZCRjVGPUY7RjVGNQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiInNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhI08hIiJGNCEiIywoLSZGKTYjIiImRi1GMkYnRjgtJkYpNiMiIihGLUYyRjJGMiooRjFGN0Y0RjgsJkY+RjJGOkY3RjIjRjIiIzc=</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIigvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIjXEY1KUkiaEdGJSIiI0Y1ISIiRjtGOEY7LCgtJkYvNiMiIidGMEY1KiZGOkY1Ri1GNUY7LSZGLzYjIiIpRjBGNUY1RjUqKiNGNSIjOUY1RjRGO0Y4RjssJkZCRjVGPUY7RjVGNQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIoNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhI1whIiJGNCEiIywoLSZGKTYjIiInRi1GMkYnRjgtJkYpNiMiIilGLUYyRjJGMiooRjFGN0Y0RjgsJkY+RjJGOkY3RjIjRjIiIzk=</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIikvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIja0Y1KUkiaEdGJSIiI0Y1ISIiRjtGOEY7LCgtJkYvNiMiIihGMEY1KiZGOkY1Ri1GNUY7LSZGLzYjIiIqRjBGNUY1RjUqKiNGNSIjO0Y1RjRGO0Y4RjssJkZCRjVGPUY7RjVGNQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIpNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhI2shIiJGNCEiIywoLSZGKTYjIiIoRi1GMkYnRjgtJkYpNiMiIipGLUYyRjJGMiooRjFGN0Y0RjgsJkY+RjJGOkY3RjIjRjIiIzs=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiovLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIjIilGNSlJImhHRiUiIiNGNSEiIkY7RjhGOywoLSZGLzYjIiIpRjBGNSomRjpGNUYtRjVGOy0mRi82IyIjNUYwRjVGNUY1KiojRjUiIz1GNUY0RjtGOEY7LCZGQkY1Rj1GO0Y1RjU=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIqNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhIyIpISIiRjQhIiMsKC0mRik2IyIiKUYtRjJGJ0Y4LSZGKTYjIiM1Ri1GMkYyRjIqKEYxRjdGNEY4LCZGPkYyRjpGN0YyI0YyIiM9</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIkKyJGNSlJImhHRiUiIiNGNSEiIkY7RjhGOywoLSZGLzYjIiIqRjBGNSomRjpGNUYtRjVGOy0mRi82IyIjNkYwRjVGNUY1KiojRjUiIz9GNUY0RjtGOEY7LCZGQkY1Rj1GO0Y1RjU=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiM1NiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhJCsiISIiRjQhIiMsKC0mRik2IyIiKkYtRjJGJ0Y4LSZGKTYjIiM2Ri1GMkYyRjIqKEYxRjdGNEY4LCZGPkYyRjpGN0YyI0YyIiM/</Equation></Text-field>
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<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u[0](t):=(solve(eq[0],u[0](t)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiE2I0kidEdGJiwmKiYjIiIiIiIkRi4tJkYlNiMiIiNGKUYuISIiKiYjIiIlRi9GLi0mRiU2I0YuRilGLkYu">LCYtJkkidUc2IjYjIiIjNiNJInRHRiYjISIiIiIkLSZGJTYjIiIiRikjIiIlRi0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u[N+1](t):=solve(eq[N+1],u[N+1](t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIzY2I0kidEdGJiIiIg==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" 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="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmRidGJyokKUkiaEdGJSIiI0YnISIiRjlGNkY5LCYqJiNGOCIiJEYnLSZGLzYjRjhGMEYnRicqJkY8RidGLUYnRjlGJ0YnKiojRidGOEYnRjRGOUY2RjksJiomIyIiJUY9RidGPkYnRicqJkZGRidGLUYnRjlGJ0Yn">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIiNiNJInRHRipGLiwmKigsJkYsRiwqJEkiaEdGKiIiIyEiIkY1RjMhIiMsJi0mRik2I0Y0Ri0jRjQiIiRGJyNGNkY8RixGLCooRjFGNUYzRjYsJkY4IyIiJUY8RicjISIlRjxGLCNGLEY0</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIiJUY1KUkiaEdGJUYnRjUhIiJGOkY4RjosKC0mRi82I0Y1RjBGNSomRidGNUYtRjVGOi0mRi82IyIiJEYwRjVGNUY1KiojRjVGN0Y1RjRGOkY4RjosJkZARjVGPEY6RjVGNQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIjNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRipGLCEiJSEiIkY0ISIjLCgtJkYpNiNGMkYtRjJGJ0Y3LSZGKTYjIiIkRi1GMkYyRjIqKEYxRjZGNEY3LCZGPEYyRjlGNkYyI0YyIiIl</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIiKkY1KUkiaEdGJSIiI0Y1ISIiRjtGOEY7LCgtJkYvNiNGOkYwRjUqJkY6RjVGLUY1RjstJkYvNiMiIiVGMEY1RjVGNSoqI0Y1IiInRjVGNEY7RjhGOywmRkFGNUY9RjtGNUY1">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIkNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhIiohIiJGNCEiIywoLSZGKTYjRjVGLUYyRidGOC0mRik2IyIiJUYtRjJGMkYyKihGMUY3RjRGOCwmRj1GMkY6RjdGMiNGMiIiJw==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIjO0Y1KUkiaEdGJSIiI0Y1ISIiRjtGOEY7LCgtJkYvNiMiIiRGMEY1KiZGOkY1Ri1GNUY7LSZGLzYjIiImRjBGNUY1RjUqKiNGNSIiKUY1RjRGO0Y4RjssJkZCRjVGPUY7RjVGNQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIlNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhIzshIiJGNCEiIywoLSZGKTYjIiIkRi1GMkYnRjgtJkYpNiMiIiZGLUYyRjJGMiooRjFGN0Y0RjgsJkY+RjJGOkY3RjIjRjIiIik=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiYvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIjREY1KUkiaEdGJSIiI0Y1ISIiRjtGOEY7LCgtJkYvNiMiIiVGMEY1KiZGOkY1Ri1GNUY7LSZGLzYjIiInRjBGNUY1RjUqKiNGNSIjNUY1RjRGO0Y4RjssJkZCRjVGPUY7RjVGNQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiImNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhI0QhIiJGNCEiIywoLSZGKTYjIiIlRi1GMkYnRjgtJkYpNiMiIidGLUYyRjJGMiooRjFGN0Y0RjgsJkY+RjJGOkY3RjIjRjIiIzU=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIicvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIjT0Y1KUkiaEdGJSIiI0Y1ISIiRjtGOEY7LCgtJkYvNiMiIiZGMEY1KiZGOkY1Ri1GNUY7LSZGLzYjIiIoRjBGNUY1RjUqKiNGNSIjN0Y1RjRGO0Y4RjssJkZCRjVGPUY7RjVGNQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiInNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhI08hIiJGNCEiIywoLSZGKTYjIiImRi1GMkYnRjgtJkYpNiMiIihGLUYyRjJGMiooRjFGN0Y0RjgsJkY+RjJGOkY3RjIjRjIiIzc=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIigvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIjXEY1KUkiaEdGJSIiI0Y1ISIiRjtGOEY7LCgtJkYvNiMiIidGMEY1KiZGOkY1Ri1GNUY7LSZGLzYjIiIpRjBGNUY1RjUqKiNGNSIjOUY1RjRGO0Y4RjssJkZCRjVGPUY7RjVGNQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIoNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhI1whIiJGNCEiIywoLSZGKTYjIiInRi1GMkYnRjgtJkYpNiMiIilGLUYyRjJGMiooRjFGN0Y0RjgsJkY+RjJGOkY3RjIjRjIiIzk=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIikvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIja0Y1KUkiaEdGJSIiI0Y1ISIiRjtGOEY7LCgtJkYvNiMiIihGMEY1KiZGOkY1Ri1GNUY7LSZGLzYjIiIqRjBGNUY1RjUqKiNGNSIjO0Y1RjRGO0Y4RjssJkZCRjVGPUY7RjVGNQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIpNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhI2shIiJGNCEiIywoLSZGKTYjIiIoRi1GMkYnRjgtJkYpNiMiIipGLUYyRjJGMiooRjFGN0Y0RjgsJkY+RjJGOkY3RjIjRjIiIzs=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiovLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIjIilGNSlJImhHRiUiIiNGNSEiIkY7RjhGOywoLSZGLzYjIiIpRjBGNSomRjpGNUYtRjVGOy0mRi82IyIjNUYwRjVGNUY1KiojRjUiIz1GNUY0RjtGOEY7LCZGQkY1Rj1GO0Y1RjU=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIqNiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhIyIpISIiRjQhIiMsKC0mRik2IyIiKUYtRjJGJ0Y4LSZGKTYjIiM1Ri1GMkYyRjIqKEYxRjdGNEY4LCZGPkYyRjpGN0YyI0YyIiM9</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqKCwmIiIiRjUqJiIkKyJGNSlJImhHRiUiIiNGNSEiIkY7RjhGOywoLSZGLzYjIiIqRjBGNSomRjpGNUYtRjVGO0Y1RjVGNUY1KiojRjUiIz9GNUY0RjtGOEY7LCZGNUY1Rj1GO0Y1RjU=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiM1NiNJInRHRipGLiwmKigsJiIiIkYyKiRJImhHRioiIiMhJCsiISIiRjQhIiMsKC0mRik2IyIiKkYtRjJGJ0Y4RjJGMkYyRjIqKEYxRjdGNEY4LCZGMkYyRjpGN0YyI0YyIiM/</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=[seq(rhs(eq[j]),j=1..N)]:</Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=[seq(u[i](t),i=1..N)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiWUc2IjcsLSZJInVHRiQ2IyIiIjYjSSJ0R0YkLSZGKDYjIiIjRistJkYoNiMiIiRGKy0mRig2IyIiJUYrLSZGKDYjIiImRistJkYoNiMiIidGKy0mRig2IyIiKEYrLSZGKDYjIiIpRistJkYoNiMiIipGKy0mRig2IyIjNUYr">NywtJkkidUc2IjYjIiIiNiNJInRHRiYtJkYlNiMiIiNGKS0mRiU2IyIiJEYpLSZGJTYjIiIlRiktJkYlNiMiIiZGKS0mRiU2IyIiJ0YpLSZGJTYjIiIoRiktJkYlNiMiIilGKS0mRiU2IyIiKkYpLSZGJTYjIiM1Rik=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=genmatrix(eqs,Y,'b1'):</Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b:=matrix(N,1):for i to N do b[i,1]:=-eval(b1[i]);od:evalm(b);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUknbWF0cml4RzYiNiM3LDcjIiIhRidGJ0YnRidGJ0YnRidGJzcjLCQqKCMiI0AiIz8iIiIsJkYvRi8qJiIkKyJGLylJImhHRiQiIiNGLyEiIkY2RjNGNkYv">PTYiNiQ7IiIiIiM1O0YmRiZFXFtsKzYkRiZGJiIiITYkIiIpRiZGKzYkIiIlRiZGKzYkIiIjRiZGKzYkRidGJiwkKiYsJkYmRiYqJEkiaEdGI0YxISQrIiEiIkY3ISIjIyIjQCIjPzYkIiInRiZGKzYkIiIkRiZGKzYkIiImRiZGKzYkIiIoRiZGKzYkIiIqRiZGKw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">h:=eval(L/(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="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=map(eval,A):</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">if N &gt; 4 then A:=map(evalf,A);end: </Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalm(A);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=exponential(A,t):</Text-field>
</Input>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=map(evalf,mat):</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y0:=matrix(N,1):for i from 1 to N do Y0[i,1]:=evalf(subs(x=i*h,rhs(IC)));od:evalm(Y0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUknbWF0cml4RzYiNiM3LDcjJCIiIUYpRidGJ0YnRidGJ0YnRidGJ0Yn">PTYiNiQ7IiIiIiM1O0YmRiZFXFtsKzYkRiZGJiQiIiFGLDYkIiIpRiZGKzYkIiIlRiZGKzYkIiIjRiZGKzYkRidGJkYrNiQiIidGJkYrNiQiIiRGJkYrNiQiIiZGJkYrNiQiIihGJkYrNiQiIipGJkYr</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">s1:=evalm(Y0+inverse(A)&amp;*b):</Text-field>
</Input>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=evalm(mat&amp;*s1-inverse(A)&amp;*b):</Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=map(simplify,Y):</Text-field>
</Input>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Digits:=10;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknRGlnaXRzRzYiIiM1">IiM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N do u[i](t):=evalf((Y[i,1]));od:</Text-field>
</Input>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 do u[i](t):=eval(u[i](t));od;</Text-field>
</Input>
<Output>
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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="Pi0mSSJ1RzYiNiMiIiM2I0kidEdGJiw4KiYkIisqeTR0TCIhIzsiIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IywkKiYkIiswYXMobyIhIidGMEYqRjAhIiJGMEY8KiYkIipVXiQ9SiEjN0YwLUYyNiMsJComJCIrbCFlL00pISIoRjBGKkYwRjxGMEYwKiYkIithTD9GOSEjNkYwLUYyNiMsJComJCIrInknPUZmRkdGMEYqRjBGPEYwRjwqJiQiKnpIVl4oISM1RjAtRjI2IywkKiYkIis/dDZtW0ZHRjBGKkYwRjxGMEYwKiYkIitjI2VnVyJGVUYwLUYyNiMsJComJCIrTWgnRylSRkdGMEYqRjBGPEYwRjwqJiQiKyNwb09bIkZVRjAtRjI2IywkKiYkIit0SERoSEZHRjBGKkYwRjxGMEYwKiYkIislZTZTJGVGS0YwLUYyNiMsJComJCIrKj5MOSY+RkdGMEYqRjBGPEYwRjwqJiQiK289VUs6RlVGMC1GMjYjLCQqJiQiKy0yeiEzIkZHRjBGKkYwRjxGMEY8KiYkIitpJkcwTiZGVUYwLUYyNiMsJComJCIrIW8oR2lWISIpRjBGKkYwRjxGMEYwKiYkIit3WFQpUSIhIipGMC1GMjYjLCQqJiQiKyIzWlpGKEZncUYwRipGMEY8RjBGPCQiKywrKys1RmdxRjA=">LDgtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErMGFzKG8iISInJCErKnk0dEwiISM7LUYkNiMsJEYrJCErbCFlL00pISIoJCIqVV4kPUohIzctRiQ2IywkRiskISsieSc9RmZGNyQhK2FMP0Y5ISM2LUYkNiMsJEYrJCErP3Q2bVtGNyQiKnpIVl4oISM1LUYkNiMsJEYrJCErTWgnRylSRjckIStjI2VnVyJGSi1GJDYjLCRGKyQhK3RIRGhIRjckIisjcG9PWyJGSi1GJDYjLCRGKyQhKyo+TDkmPkY3JCErJWU2UyRlRkItRiQ2IywkRiskISstMnohMyJGNyQhK289VUs6RkotRiQ2IywkRiskISshbyhHaVYhIikkIitpJkcwTiZGSi1GJDYjLCRGKyQhKyIzWlpGKCEiKiQhK3dYVClRIkZecCQiKywrKys1Rl5wIiIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDgtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErMGFzKG8iISInJCIrZj9QUjchIzotRiQ2IywkRiskIStsIWUvTSkhIigkISt4V1k9NiEjNy1GJDYjLCRGKyQhKyJ5Jz1GZkY3JCIrKnkkZStHISM2LUYkNiMsJEYrJCErP3Q2bVtGNyQhKiYzSCozKiEjNS1GJDYjLCRGKyQhK01oJ0cpUkY3JCIra0tqI3AoRkItRiQ2IywkRiskISt0SERoSEY3JCIrUiQ9R10nRkItRiQ2IywkRiskISsqPkw5Jj5GNyQhK0JhZmY+RkotRiQ2IywkRiskISstMnohMyJGNyQiK3d2Wlk4RkotRiQ2IywkRiskISshbyhHaVYhIikkIitKWzIjbyNGSi1GJDYjLCRGKyQhKyIzWlpGKCEiKiQhKyM0WVtHIkZecCQiKywrKys1Rl5wIiIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDgtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErMGFzKG8iISInJCErdHMqeTkiISM5LUYkNiMsJEYrJCErbCFlL00pISIoJCIrNTlfd1IhIzctRiQ2IywkRiskISsieSc9RmZGNyQhK1w0empdISM2LUYkNiMsJEYrJCErP3Q2bVtGNyQiKngjKj4wKSEjNS1GJDYjLCRGKyQhK01oJ0cpUkY3JCIrKmUnb0VNRkItRiQ2IywkRiskISt0SERoSEY3JCErUnVpMjdGSi1GJDYjLCRGKyQhKyo+TDkmPkY3JCErbjc1X1ZGQi1GJDYjLCRGKyQhKy0yeiEzIkY3JCIrcyVHJ1tDRkotRiQ2IywkRiskISshbyhHaVYhIikkIitrLiJvKCkpISM4LUYkNiMsJEYrJCErIjNaWkYoISIqJCErRzllXDZGX3AkIissKysrNUZfcCIiIg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDgtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErMGFzKG8iISInJCIrQyR5OC0iISM4LUYkNiMsJEYrJCErbCFlL00pISIoJCErVGdMPzghIzYtRiQ2IywkRiskISsieSc9RmZGNyQiKlA0RyZ6ISM1LUYkNiMsJEYrJCErP3Q2bVtGNyQhKyU+X05mJEY6LUYkNiMsJEYrJCErTWgnRylSRjckISsoR0U8ZilGOi1GJDYjLCRGKyQhK3RIRGhIRjckIStfaygpSFBGOi1GJDYjLCRGKyQhKyo+TDkmPkY3JCIrPmUjPUgiRkItRiQ2IywkRiskISstMnohMyJGNyQiKy1leT07RkItRiQ2IywkRiskISshbyhHaVYhIikkIStlKVxGMiNGQi1GJDYjLCRGKyQhKyIzWlpGKCEiKiQhK3ciUTEiKipGQiQiKy0rKys1Rl1wIiIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDgtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErMGFzKG8iISInJCErW1JLQyQpISM4LUYkNiMsJEYrJCErbCFlL00pISIoJCIrSFZDUVEhIzYtRiQ2IywkRiskISsieSc9RmZGNyQhKl49YFwqISM1LUYkNiMsJEYrJCErP3Q2bVtGNyQhKyEzbCIpcCNGOi1GJDYjLCRGKyQhK01oJ0cpUkY3JCIrQFxDdD5GOi1GJDYjLCRGKyQhK3RIRGhIRjckIipHbkJvKkZCLUYkNiMsJEYrJCErKj5MOSY+RjckIisrUEAtN0ZCLUYkNiMsJEYrJCErLTJ6ITMiRjckISslUid5STVGOi1GJDYjLCRGKyQhKyFvKEdpViEiKSQhK3RbJ3BCJEZCLUYkNiMsJEYrJCErIjNaWkYoISIqJCErQj8iUj0pRkIkIistKysrNUZdcCIiIg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDgtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErMGFzKG8iISInJCIrRCZ5ZCFmISM3LUYkNiMsJEYrJCErbCFlL00pISIoJCErW09dXyopISM2LUYkNiMsJEYrJCErInknPUZmRjckIio4TTwhZiEjNS1GJDYjLCRGKyQhKz90Nm1bRjckIityUV0lNCZGOi1GJDYjLCRGKyQhK01oJ0cpUkY3JCIrZidRV3EnRjotRiQ2IywkRiskISt0SERoSEY3JCIrQG81a2NGOi1GJDYjLCRGKyQhKyo+TDkmPkY3JCErJSllbjM4RjotRiQ2IywkRiskISstMnohMyJGNyQhKzgrQCs6RkItRiQ2IywkRiskISshbyhHaVYhIikkISthYFZsTUZCLUYkNiMsJEYrJCErIjNaWkYoISIqJCErNnl0LmtGQiQiKy0rKys1Rl1wIiIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDgtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErMGFzKG8iISInJCErdCgqSCtNISM2LUYkNiMsJEYrJCErbCFlL00pISIoJCIrQXhPQjkhIzUtRiQ2IywkRiskISsieSc9RmZGNyQiKzFMRCE+JEYxLUYkNiMsJEYrJCErP3Q2bVtGNyQiKzwmKkhzWSEjNy1GJDYjLCRGKyQhK01oJ0cpUkY3JCErJUhHKFs5RjEtRiQ2IywkRiskISt0SERoSEY3JCErTmRmOGJGMS1GJDYjLCRGKyQhKyo+TDkmPkY3JCErd21KcDZGOi1GJDYjLCRGKyQhKy0yeiEzIkY3JCErVltbbT5GOi1GJDYjLCRGKyQhKyFvKEdpViEiKSQhK08iPSdwSEY6LUYkNiMsJEYrJCErIjNaWkYoISIqJCEraVc0WllGOiQiKy0rKys1Rl1wIiIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDgtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErMGFzKG8iISInJCIrJlI6MVQiISM1LUYkNiMsJEYrJCErbCFlL00pISIoJCErJz4kRzIpKSEjNi1GJDYjLCRGKyQhKyJ5Jz1GZkY3JCErMUBESGhGOi1GJDYjLCRGKyQhKz90Nm1bRjckIStORHBsV0Y6LUYkNiMsJEYrJCErTWgnRylSRjckIStLTS9BbEY6LUYkNiMsJEYrJCErdEhEaEhGNyQhK1ZJdUMlKkY6LUYkNiMsJEYrJCErKj5MOSY+RjckIStSaWZbN0YxLUYkNiMsJEYrJCErLTJ6ITMiRjckIStBLk8sO0YxLUYkNiMsJEYrJCErIW8oR2lWISIpJCErPlwhZTAjRjEtRiQ2IywkRiskISsiM1paRighIiokIStCcz90SEYxJCIrLCsrKzVGXHAiIiI=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDgtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErMGFzKG8iISInJCErY0soXD0kISM1LUYkNiMsJEYrJCErbCFlL00pISIoJCErX2cuVDVGMS1GJDYjLCRGKyQhKyJ5Jz1GZkY3JCErPC4pZTEmISM2LUYkNiMsJEYrJCErP3Q2bVtGNyQhKylvI0hXS0ZBLUYkNiMsJEYrJCErTWgnRylSRjckIStMLlVoVkZBLUYkNiMsJEYrJCErdEhEaEhGNyQhK1U7NnFjRkEtRiQ2IywkRiskISsqPkw5Jj5GNyQhK00uKXojcEZBLUYkNiMsJEYrJCErLTJ6ITMiRjckISt6VipIQSlGQS1GJDYjLCRGKyQhKyFvKEdpViEiKSQhK2tLKTQsIkYxLUYkNiMsJEYrJCErIjNaWkYoISIqJCErQTVOPjlGMSQiKywrKys1RlxwIiIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIzY2I0kidEdGJiIiIg==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L79" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Set the colors for the curves:</Text-field>
</Input>
</Group>
<Group labelreference="L80" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">setcolors([&quot;Red&quot;, &quot;Blue&quot;, &quot;LimeGreen&quot;, &quot;Goldenrod&quot;, &quot;maroon&quot;, &quot;DarkTurquoise&quot;, &quot;coral&quot;, &quot;aquamarine&quot;, &quot;magenta&quot;, &quot;khaki&quot;,  &quot;sienna&quot;, &quot;orange&quot;, &quot;yellow&quot;, &quot;gray&quot;]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyhRJFJlZDYiUSpMaW1lR3JlZW5GJFEqR29sZGVucm9kRiRRJUJsdWVGJFEtTWVkaXVtT3JjaGlkRiRRLkRhcmtUdXJxdW9pc2VGJA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pp:=plot([seq(u[i](t),i=0..N+1)],t=0..0.4,thickness=3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 19140 characters]">[encoded data, 19112 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L81" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Plot the texts for the corresponding curves:</Text-field>
</Input>
</Group>
<Group labelreference="L82" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">arw:=arrow(&lt;0.15,0.4&gt;,&lt;-0.05,0.63&gt;,width=[1/700,relative=true],head_width=[1/200,relative=false],head_length=[1/30,relative=false]):
pt:=textplot([[0.25,0.35,typeset(&quot;Follow the arrow: &quot;,u[0],&quot;(t), ..., &quot;,u[N+1],&quot;(t).&quot;)]]):</Text-field>
</Input>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display([pp,pt,arw],axes=boxed,title=&quot;Figure Exp. 5.19.&quot;,labels=[t,&quot;u&quot;]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">[encoded data, 35344 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tf:=0.2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdGZHNiIkIiIjISIi">JCIiIyEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">M:=30;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTUc2IiIjSQ==">IiNJ</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T1:=[seq(tf*i/M,i=0..M)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVDFHNiI3QSQiIiFGJyQiK25tbW1tISM3JCIrTExMTDghIzYkIisrKysrP0YtJCIrbm1tbUVGLSQiK0xMTExMRi0kIisrKysrU0YtJCIrbm1tbVlGLSQiK0xMTExgRi0kIisrKysrZ0YtJEYpRi0kIitMTExMdEYtJCIrKysrKyEpRi0kIitubW1tJylGLSQiK0xMTEwkKkYtJCIrKysrKzUhIzUkIitubW1tNUZHJCIrTExMTDZGRyQiKysrKys3RkckIitubW1tN0ZHJEYsRkckIisrKysrOUZHJCIrbm1tbTlGRyQiK0xMTEw6RkckIisrKysrO0ZHJCIrbm1tbTtGRyQiK0xMTEw8RkckIisrKysrPUZHJCIrbm1tbT1GRyQiK0xMTEw+RkckRi9GRw==">N0EkIiIhRiQkIitubW1tbSEjNyQiK0xMTEw4ISM2JCIrKysrKz9GKiQiK25tbW1FRiokIitMTExMTEYqJCIrKysrK1NGKiQiK25tbW1ZRiokIitMTExMYEYqJCIrKysrK2dGKiRGJkYqJCIrTExMTHRGKiQiKysrKyshKUYqJCIrbm1tbScpRiokIitMTExMJCpGKiQiKysrKys1ISM1JCIrbm1tbTVGRCQiK0xMTEw2RkQkIisrKysrN0ZEJCIrbm1tbTdGRCRGKUZEJCIrKysrKzlGRCQiK25tbW05RkQkIitMTExMOkZEJCIrKysrKztGRCQiK25tbW07RkQkIitMTExMPEZEJCIrKysrKz1GRCQiK25tbW09RkQkIitMTExMPkZEJEYsRkQ=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">PP:=matrix(N+2,M+1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjUFBHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIzc7RioiI0o3Ig==">PTYiNiQ7IiIiIiM3O0YmIiNKRVxbbCE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N+2 do PP[i,1]:=evalf(subs(x=(i-1)*h,rhs(IC)));od:</Text-field>
</Input>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N+2 do for j from 2 to M+1 do PP[i,j]:=evalf(subs(t=T1[j],u[i-1](t)));od;od:</Text-field>
</Input>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plotdata := [seq([ seq([(i-1)*h,T1[j],PP[i,j]], i=1..N+2)], j=1..M+1)]:</Text-field>
</Input>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">surfdata(plotdata,axes=boxed,title=&quot;Figure Exp. 5.20.&quot;,labels=[x,t,u],orientation=[-135,45]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="three-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0">[encoded data, 17600 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 do u[i](z):=subs(t=z/2/Pe,u[i](t));od:</Text-field>
</Input>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pp:=plot([seq(subs(Pe=1,u[i](z)),i=0..N+1)],z=0..1,thickness=3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 19828 characters]">[encoded data, 19788 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L84" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Plot the texts for the corresponding curves:</Text-field>
</Input>
</Group>
<Group labelreference="L85" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">arw:=arrow(&lt;0.3,0.4&gt;,&lt;-0.15,0.63&gt;,width=[1/700,relative=true],head_width=[1/150,relative=false],head_length=[1/30,relative=false]):
pt:=textplot([[0.55,0.35,typeset(&quot;Follow the arrow: &quot;,u[0],&quot;(z), ..., &quot;,u[N+1],&quot;(z).&quot;)]]):</Text-field>
</Input>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">
display([pp,pt,arw],axes=boxed,title=&quot;Figure Exp. 5.21.&quot;,labels=[z,&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, 36124 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tf:=1.;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdGZHNiIkIiIiIiIh">JCIiIiIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">M:=30;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTUc2IiIjSQ==">IiNJ</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L54" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T1:=[seq(tf*i/M,i=0..M)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVDFHNiI3QSQiIiFGJyQiK0xMTExMISM2JCIrbm1tbW1GKiQiKysrKys1ISM1JCIrTExMTDhGLyQiK25tbW07Ri8kIisrKysrP0YvJCIrTExMTEJGLyQiK25tbW1FRi8kIisrKysrSUYvJEYpRi8kIitubW1tT0YvJCIrKysrK1NGLyQiK0xMTExWRi8kIitubW1tWUYvJCIrKysrK11GLyQiK0xMTExgRi8kIitubW1tY0YvJCIrKysrK2dGLyQiK0xMTExqRi8kRixGLyQiKysrKytxRi8kIitMTExMdEYvJCIrbm1tbXdGLyQiKysrKyshKUYvJCIrTExMTCQpRi8kIitubW1tJylGLyQiKysrKyshKkYvJCIrTExMTCQqRi8kIitubW1tJypGLyRGLiEiKg==">N0EkIiIhRiQkIitMTExMTCEjNiQiK25tbW1tRickIisrKysrNSEjNSQiK0xMTEw4RiwkIitubW1tO0YsJCIrKysrKz9GLCQiK0xMTExCRiwkIitubW1tRUYsJCIrKysrK0lGLCRGJkYsJCIrbm1tbU9GLCQiKysrKytTRiwkIitMTExMVkYsJCIrbm1tbVlGLCQiKysrKytdRiwkIitMTExMYEYsJCIrbm1tbWNGLCQiKysrKytnRiwkIitMTExMakYsJEYpRiwkIisrKysrcUYsJCIrTExMTHRGLCQiK25tbW13RiwkIisrKysrISlGLCQiK0xMTEwkKUYsJCIrbm1tbScpRiwkIisrKysrISpGLCQiK0xMTEwkKkYsJCIrbm1tbScqRiwkRishIio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L55" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">PP:=matrix(N+2,M+1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjUFBHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIzc7RioiI0o3Ig==">PTYiNiQ7IiIiIiM3O0YmIiNKRVxbbCE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N+2 do PP[i,1]:=evalf(subs(x=(i-1)*h,rhs(IC)));od:</Text-field>
</Input>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N+2 do for j from 2 to M+1 do PP[i,j]:=evalf(subs(z=T1[j],Pe=1.,u[i-1](z)));od;od:</Text-field>
</Input>
</Group>
<Group labelreference="L58" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plotdata := [seq([ seq([(i-1)*h,T1[j],PP[i,j]], i=1..N+2)], j=1..M+1)]:</Text-field>
</Input>
</Group>
<Group labelreference="L59" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">surfdata(plotdata,axes=boxed,title=&quot;Figure 5.22.&quot;,labels=[x,z,u],orientation=[-135,45]);</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, 17788 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L60" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pp:=plot([seq(subs(Pe=10,u[i](z)),i=0..N+1)],z=0..1,thickness=3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 17528 characters]">[encoded data, 17504 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L61" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display([pp],axes=boxed,title=&quot;Figure Exp. 5.23.&quot;,labels=[z,&quot;u&quot;],caption=typeset(&quot;From the bottom to the top of the figure: &quot;,u[0],&quot;(z), ..., &quot;,u[N+1],&quot;(z)&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, 33540 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L62" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tf:=1.;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdGZHNiIkIiIiIiIh">JCIiIiIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L63" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">M:=30;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTUc2IiIjSQ==">IiNJ</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L64" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T1:=[seq(tf*i/M,i=0..M)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVDFHNiI3QSQiIiFGJyQiK0xMTExMISM2JCIrbm1tbW1GKiQiKysrKys1ISM1JCIrTExMTDhGLyQiK25tbW07Ri8kIisrKysrP0YvJCIrTExMTEJGLyQiK25tbW1FRi8kIisrKysrSUYvJEYpRi8kIitubW1tT0YvJCIrKysrK1NGLyQiK0xMTExWRi8kIitubW1tWUYvJCIrKysrK11GLyQiK0xMTExgRi8kIitubW1tY0YvJCIrKysrK2dGLyQiK0xMTExqRi8kRixGLyQiKysrKytxRi8kIitMTExMdEYvJCIrbm1tbXdGLyQiKysrKyshKUYvJCIrTExMTCQpRi8kIitubW1tJylGLyQiKysrKyshKkYvJCIrTExMTCQqRi8kIitubW1tJypGLyRGLiEiKg==">N0EkIiIhRiQkIitMTExMTCEjNiQiK25tbW1tRickIisrKysrNSEjNSQiK0xMTEw4RiwkIitubW1tO0YsJCIrKysrKz9GLCQiK0xMTExCRiwkIitubW1tRUYsJCIrKysrK0lGLCRGJkYsJCIrbm1tbU9GLCQiKysrKytTRiwkIitMTExMVkYsJCIrbm1tbVlGLCQiKysrKytdRiwkIitMTExMYEYsJCIrbm1tbWNGLCQiKysrKytnRiwkIitMTExMakYsJEYpRiwkIisrKysrcUYsJCIrTExMTHRGLCQiK25tbW13RiwkIisrKysrISlGLCQiK0xMTEwkKUYsJCIrbm1tbScpRiwkIisrKysrISpGLCQiK0xMTEwkKkYsJCIrbm1tbScqRiwkRishIio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L65" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">PP:=matrix(N+2,M+1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjUFBHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIzc7RioiI0o3Ig==">PTYiNiQ7IiIiIiM3O0YmIiNKRVxbbCE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L66" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N+2 do PP[i,1]:=evalf(subs(x=(i-1)*h,rhs(IC)));od:</Text-field>
</Input>
</Group>
<Group labelreference="L67" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N+2 do for j from 2 to M+1 do PP[i,j]:=evalf(subs(z=T1[j],Pe=10.,u[i-1](z)));od;od:</Text-field>
</Input>
</Group>
<Group labelreference="L68" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plotdata:= [seq([ seq([(i-1)*h,T1[j],PP[i,j]], i=1..N+2)], j=1..M+1)]:</Text-field>
</Input>
</Group>
<Group labelreference="L69" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">surfdata(plotdata,axes=boxed,title=&quot;Figure Exp. 5.24.&quot;,labels=[x,z,u],orientation=[-135,45]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="three-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0">[encoded data, 17392 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L70" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ua0:=1-1.477*exp(-3.658*z/Pe)+0.81*exp(-22.178*z/Pe)-0.385*exp(-53.05*z/Pe);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkdWEwRzYiLCoiIiJGJiomJCIleDkhIiRGJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCQqKCQiJWVPRipGJkkiekdGJEYmSSNQZUdGJCEiIkY3RiZGNyomJCIjIikhIiNGJi1GLDYjLCQqKCQiJnlAI0YqRiZGNUYmRjZGN0Y3RiZGJiomJCIkJlFGKkYmLUYsNiMsJCooJCIlMGBGO0YmRjVGJkY2RjdGN0YmRjc=">LCoiIiJGIy1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJkkiekdGKUYjSSNQZUdGKSEiIiQhJWVPISIkJCEleDlGMi1GJTYjLCRGLCQhJnlAI0YyJCIjIikhIiMtRiU2IywkRiwkISUwYEY8JCEkJlFGMg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L71" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u[0](z);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L72" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:=[0.1,0.2,0.25,0.5,1,2];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjcoJCIiIiEiIiQiIiNGKCQiI0QhIiMkIiImRihGJ0Yq">NygkIiIiISIiJCIiI0YlJCIjRCEiIyQiIiZGJUYkRic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L73" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">M:=nops(pars);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTUc2IiIiJw==">IiIn</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L74" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">seq(evalf(subs(z=Pe*pars[i],ua0)),i=1..M);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NigkIisjW1ZZPCchIzYkIitbcVgqKUghIzUkIiteaTE4VEYoJCIrdVtXR3dGKCQiKyEqKXAiPicqRigkIitsMT0hKioqRig=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L75" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">seq(evalf(subs(z=Pe*pars[i],z=10,u[0](z))),i=1..M);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NigkIiovWWVAJyEjNSQiKysoUlwoSEYlJCIrVUBvIzQlRiUkIiswYysyd0YlJCIrdSt1NicqRiUkIityL3kqKSoqRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L76" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>