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<Text-field style="Text" layout="Normal"> Example 5.2.6 The Shrinking Core Model for Catalyst Regeneration</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart;</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(linalg):with(plots):</Text-field>
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<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ge:=diff(u(x,t),t)=diff(u(x,t),x$2)+2/x*diff(u(x,t),x);</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZ2VHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkidEdGJEYuLCYtRic2JEYqLUkiJEdGKDYkRi0iIiMiIiIqKEY1RjZGLSEiIi1GJzYkRipGLUY2RjY=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLCwmLUYkNiQtRiQ2JEYnRitGKyIiIiooIiIjRjJGKyEiIkYwRjJGMg==</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,t)-0;</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLUkidUdGJDYkSSJ4R0YkSSJ0R0Yk">LUkidUc2IjYkSSJ4R0YkSSJ0R0Yk</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>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLCYtSSJ1R0YkNiRJInhHRiRJInRHRiQiIiJGKyEiIg==">LCYtSSJ1RzYiNiRJInhHRiVJInRHRiUiIiJGKSEiIg==</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IC:=u(x,0)=0;</Text-field>
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<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">ge2:=diff(xc[1](t),t)=-k*diff(u(x,t),x);</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZ2UyRzYiLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkjeGNHRiQ2IyIiIjYjSSJ0R0YkRjAsJComSSJrR0YkRi4tRic2JC1JInVHRiQ2JEkieEdGJEYwRjlGLiEiIg==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkjeGNHNiI2IyIiIjYjSSJ0R0YqRi4sJComSSJrR0YqRiwtRiQ2JC1JInVHRio2JEkieEdGKkYuRjdGLCEiIg==</Equation></Text-field>
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<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">k:=0.1;</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkia0c2IiQiIiIhIiI=">JCIiIiEiIg==</Equation></Text-field>
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<Group labelreference="L10" 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="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">L:=1;</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTEc2IiIiIg==">IiIi</Equation></Text-field>
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<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>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGZHNiIsJCooIyIiIiIiI0YoLCgtJkkidUdGJDYjRik2I0kidEdGJCEiIiomIiIkRigtJkYtNiMiIiFGL0YoRjEqJiIiJUYoLSZGLTYjRihGL0YoRihGKEkiaEdGJEYxRig=">LCQqKCMiIiIiIiNGJSwoLSZJInVHNiI2I0YmNiNJInRHRishIiIqJiIiJEYlLSZGKjYjIiIhRi1GJUYvKiYiIiVGJS0mRio2I0YlRi1GJUYlRiVJImhHRitGL0Yl</Equation></Text-field>
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<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>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGJHNiIsJCooIyIiIiIiI0YoLCgtJkkidUdGJDYjIiIqNiNJInRHRiRGKComIiIkRigtJkYtNiMiIzZGMEYoRigqJiIiJUYoLSZGLTYjIiM1RjBGKCEiIkYoSSJoR0YkRj5GKA==">LCQqKCMiIiIiIiNGJSwoLSZJInVHNiI2IyIiKjYjSSJ0R0YrRiUqJiIiJEYlLSZGKjYjIiM2Ri5GJUYlKiYiIiVGJS0mRio2IyIjNUYuRiUhIiJGJUkiaEdGK0Y8RiU=</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydx:=1/2/h*(u[m+1](t)-u[m-1](t));</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklZHlkeEc2IiwkKigjIiIiIiIjRihJImhHRiQhIiIsJi0mSSJ1R0YkNiMsJkkibUdGJEYoRihGKDYjSSJ0R0YkRigtJkYvNiMsJkYyRihGKEYrRjNGK0YoRig=">LCQqKCMiIiIiIiNGJUkiaEc2IiEiIiwmLSZJInVHRig2IywmSSJtR0YoRiVGJUYlNiNJInRHRihGJS0mRi02IywmRjBGJUYlRilGMUYpRiVGJQ==</Equation></Text-field>
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<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>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknZDJ5ZHgyRzYiKiYpSSJoR0YkIiIjISIiLCgtJkkidUdGJDYjLCZJIm1HRiQiIiJGMUYpNiNJInRHRiRGMSomRihGMS0mRi02I0YwRjJGMUYpLSZGLTYjLCZGMEYxRjFGMUYyRjFGMQ==">KiYpSSJoRzYiIiIjISIiLCgtJkkidUdGJTYjLCZJIm1HRiUiIiJGL0YnNiNJInRHRiVGLyomRiZGLy0mRis2I0YuRjBGL0YnLSZGKzYjLCZGLkYvRi9GL0YwRi9GLw==</Equation></Text-field>
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<Group labelreference="L16" 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),bc1);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLSZJInVHRiQ2IyIiITYjSSJ0R0Yk">LSZJInVHNiI2IyIiITYjSSJ0R0Yl</Equation></Text-field>
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<Group labelreference="L17" 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),bc2);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLCYtJkkidUdGJDYjIiM2NiNJInRHRiQiIiJGLSEiIg==">LCYtJkkidUc2IjYjIiM2NiNJInRHRiYiIiJGKyEiIg==</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqX:=subs(diff(u(x,t),x)=dydxf,u(x,t)=u[0](t),ge2);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFYRzYiLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkjeGNHRiQ2IyIiIjYjSSJ0R0YkRjAsJCooJCIrKysrK10hIzZGLiwoLSZJInVHRiQ2IyIiI0YvISIiKiYiIiRGLi0mRjk2IyIiIUYvRi5GPComIiIlRi4tJkY5Ri1GL0YuRi5GLkkiaEdGJEY8Rjw=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkjeGNHNiI2IyIiIjYjSSJ0R0YqRi4sJCooJCIrKysrK10hIzZGLCwoLSZJInVHRio2IyIiI0YtISIiKiYiIiRGLC0mRjc2IyIiIUYtRixGOiomIiIlRiwtJkY3RitGLUYsRixGLEkiaEdGKkY6Rjo=</Equation></Text-field>
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<Group labelreference="L19" 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="PiZJI2VxRzYiNiMiIiEtJkkidUdGJUYmNiNJInRHRiU=">LSZJInVHNiI2IyIiITYjSSJ0R0Yl</Equation></Text-field>
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<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[N+1]:=bc2; </Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzYsJi0mSSJ1R0YlRiY2I0kidEdGJSIiIkYuISIi">LCYtJkkidUc2IjYjIiM2NiNJInRHRiYiIiJGKyEiIg==</Equation></Text-field>
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<Group labelreference="L21" 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=xc[1](t)+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="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJImhHRiUiIiMhIiIsKC0mRi82IyIiIUYwRicqJkY2RidGLUYnRjctJkYvNiNGNkYwRidGJ0YnKigsJi0mSSN4Y0dGJUYmRjBGJ0Y1RidGN0Y1RjcsJkY+RidGOUY3RidGJw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIiNiNJInRHRipGLiwmKiYpSSJoR0YqIiIjISIiLCgtJkYpNiMiIiFGLUYsKiZGM0YsRidGLEY0LSZGKTYjRjNGLUYsRixGLCooLCYtJkkjeGNHRipGK0YtRixGMkYsRjRGMkY0LCZGO0YsRjZGNEYsRiw=</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="PiZJI2VxRzYiNiMiIikvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJImhHRiUiIiMhIiIsKC0mRi82IyIiKEYwIiIiKiZGNkY9Ri1GPUY3LSZGLzYjIiIqRjBGPUY9Rj0qKCwmLSZJI3hjR0YlNiNGPUYwRj0qJkYnRj1GNUY9Rj1GN0Y1RjcsJkY/Rj1GOUY3Rj1GPQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIpNiNJInRHRipGLiwmKiYpSSJoR0YqIiIjISIiLCgtJkYpNiMiIihGLSIiIiomRjNGOkYnRjpGNC0mRik2IyIiKkYtRjpGOkY6KigsJi0mSSN4Y0dGKjYjRjpGLUY6KiZGLEY6RjJGOkY6RjRGMkY0LCZGPEY6RjZGNEY6Rjo=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiovLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJImhHRiUiIiMhIiIsKC0mRi82IyIiKUYwIiIiKiZGNkY9Ri1GPUY3LSZGLzYjIiM1RjBGPUY9Rj0qKCwmLSZJI3hjR0YlNiNGPUYwRj0qJkYnRj1GNUY9Rj1GN0Y1RjcsJkY/Rj1GOUY3Rj1GPQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIqNiNJInRHRipGLiwmKiYpSSJoR0YqIiIjISIiLCgtJkYpNiMiIilGLSIiIiomRjNGOkYnRjpGNC0mRik2IyIjNUYtRjpGOkY6KigsJi0mSSN4Y0dGKjYjRjpGLUY6KiZGLEY6RjJGOkY6RjRGMkY0LCZGPEY6RjZGNEY6Rjo=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJImhHRiUiIiMhIiIsKC0mRi82IyIiKkYwIiIiKiZGNkY9Ri1GPUY3LSZGLzYjIiM2RjBGPUY9Rj0qKCwmLSZJI3hjR0YlNiNGPUYwRj0qJkYnRj1GNUY9Rj1GN0Y1RjcsJkY/Rj1GOUY3Rj1GPQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiM1NiNJInRHRipGLiwmKiYpSSJoR0YqIiIjISIiLCgtJkYpNiMiIipGLSIiIiomRjNGOkYnRjpGNC0mRik2IyIjNkYtRjpGOkY6KigsJi0mSSN4Y0dGKjYjRjpGLUY6KiZGLEY6RjJGOkY6RjRGMkY0LCZGPEY6RjZGNEY6Rjo=</Equation></Text-field>
</Output>
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<Group labelreference="L22" 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="Pi0mSSJ1RzYiNiMiIiE2I0kidEdGJkYo">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" 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="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">h:=(1-xc[1](t))/(N+1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiaEc2IiwmIyIiIiIjNkYnKiZGJkYnLSZJI3hjR0YkNiNGJzYjSSJ0R0YkRichIiI=">LCYjIiIiIiM2RiQqJkYjRiQtJkkjeGNHNiI2I0YkNiNJInRHRipGJCEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N do eq[i]:=eval(eq[i]);od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJiksJiNGJyIjNkYnKiZGNkYnLSZJI3hjR0YlRiZGMEYnISIiIiIjRjwsJiomRj1GJ0YtRidGPC0mRi82I0Y9RjBGJ0YnRicqKCwmKiYjIiM1RjdGJ0Y5RidGJ0Y2RidGPEY1RjxGQEYnRic=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIiNiNJInRHRipGLiwmKiYpLCYjRiwiIzZGLComRjNGLC0mSSN4Y0dGKkYrRi1GLCEiIiIiI0Y5LCYqJkY6RixGJ0YsRjktJkYpNiNGOkYtRixGLEYsKigsJiomIyIjNUY0RixGNkYsRixGM0YsRjlGMkY5Rj1GLEYs</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJiksJiMiIiIiIzZGNyomRjZGNy0mSSN4Y0dGJTYjRjdGMEY3ISIiRidGPiwoLSZGL0Y9RjBGNyomRidGN0YtRjdGPi0mRi82IyIiJEYwRjdGN0Y3KigsJiomIyIiKkY4RjdGOkY3RjcjRidGOEY3Rj5GNUY+LCZGQ0Y3RkBGPkY3Rjc=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIjNiNJInRHRipGLiwmKiYpLCYjIiIiIiM2RjQqJkYzRjQtJkkjeGNHRio2I0Y0Ri1GNCEiIkYsRjssKC0mRilGOkYtRjQqJkYsRjRGJ0Y0RjstJkYpNiMiIiRGLUY0RjRGNCooLCYqJiMiIipGNUY0RjdGNEY0I0YsRjVGNEY7RjJGOywmRkBGNEY9RjtGNEY0</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJiksJiMiIiIiIzZGNyomRjZGNy0mSSN4Y0dGJTYjRjdGMEY3ISIiIiIjRj4sKC0mRi82I0Y/RjBGNyomRj9GN0YtRjdGPi0mRi82IyIiJUYwRjdGN0Y3KigsJiomIyIiKUY4RjdGOkY3RjcjRidGOEY3Rj5GNUY+LCZGRUY3RkFGPkY3Rjc=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIkNiNJInRHRipGLiwmKiYpLCYjIiIiIiM2RjQqJkYzRjQtJkkjeGNHRio2I0Y0Ri1GNCEiIiIiI0Y7LCgtJkYpNiNGPEYtRjQqJkY8RjRGJ0Y0RjstJkYpNiMiIiVGLUY0RjRGNCooLCYqJiMiIilGNUY0RjdGNEY0I0YsRjVGNEY7RjJGOywmRkJGNEY+RjtGNEY0</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJiksJiMiIiIiIzZGNyomRjZGNy0mSSN4Y0dGJTYjRjdGMEY3ISIiIiIjRj4sKC0mRi82IyIiJEYwRjcqJkY/RjdGLUY3Rj4tJkYvNiMiIiZGMEY3RjdGNyooLCYqJiMiIihGOEY3RjpGN0Y3I0YnRjhGN0Y+RjVGPiwmRkZGN0ZBRj5GN0Y3">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIlNiNJInRHRipGLiwmKiYpLCYjIiIiIiM2RjQqJkYzRjQtJkkjeGNHRio2I0Y0Ri1GNCEiIiIiI0Y7LCgtJkYpNiMiIiRGLUY0KiZGPEY0RidGNEY7LSZGKTYjIiImRi1GNEY0RjQqKCwmKiYjIiIoRjVGNEY3RjRGNCNGLEY1RjRGO0YyRjssJkZDRjRGPkY7RjRGNA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiYvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJiksJiMiIiIiIzZGNyomRjZGNy0mSSN4Y0dGJTYjRjdGMEY3ISIiIiIjRj4sKC0mRi82IyIiJUYwRjcqJkY/RjdGLUY3Rj4tJkYvNiMiIidGMEY3RjdGNyooLCYqJiNGSUY4RjdGOkY3RjcjRidGOEY3Rj5GNUY+LCZGRkY3RkFGPkY3Rjc=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiImNiNJInRHRipGLiwmKiYpLCYjIiIiIiM2RjQqJkYzRjQtJkkjeGNHRio2I0Y0Ri1GNCEiIiIiI0Y7LCgtJkYpNiMiIiVGLUY0KiZGPEY0RidGNEY7LSZGKTYjIiInRi1GNEY0RjQqKCwmKiYjRkZGNUY0RjdGNEY0I0YsRjVGNEY7RjJGOywmRkNGNEY+RjtGNEY0</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIicvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJiksJiMiIiIiIzZGNyomRjZGNy0mSSN4Y0dGJTYjRjdGMEY3ISIiIiIjRj4sKC0mRi82IyIiJkYwRjcqJkY/RjdGLUY3Rj4tJkYvNiMiIihGMEY3RjdGNyooLCYqJiNGREY4RjdGOkY3RjcjRidGOEY3Rj5GNUY+LCZGRkY3RkFGPkY3Rjc=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiInNiNJInRHRipGLiwmKiYpLCYjIiIiIiM2RjQqJkYzRjQtJkkjeGNHRio2I0Y0Ri1GNCEiIiIiI0Y7LCgtJkYpNiMiIiZGLUY0KiZGPEY0RidGNEY7LSZGKTYjIiIoRi1GNEY0RjQqKCwmKiYjRkFGNUY0RjdGNEY0I0YsRjVGNEY7RjJGOywmRkNGNEY+RjtGNEY0</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIigvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJiksJiMiIiIiIzZGNyomRjZGNy0mSSN4Y0dGJTYjRjdGMEY3ISIiIiIjRj4sKC0mRi82IyIiJ0YwRjcqJkY/RjdGLUY3Rj4tJkYvNiMiIilGMEY3RjdGNyooLCYqJiMiIiVGOEY3RjpGN0Y3I0YnRjhGN0Y+RjVGPiwmRkZGN0ZBRj5GN0Y3">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIoNiNJInRHRipGLiwmKiYpLCYjIiIiIiM2RjQqJkYzRjQtJkkjeGNHRio2I0Y0Ri1GNCEiIiIiI0Y7LCgtJkYpNiMiIidGLUY0KiZGPEY0RidGNEY7LSZGKTYjIiIpRi1GNEY0RjQqKCwmKiYjIiIlRjVGNEY3RjRGNCNGLEY1RjRGO0YyRjssJkZDRjRGPkY7RjRGNA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIikvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJiksJiMiIiIiIzZGNyomRjZGNy0mSSN4Y0dGJTYjRjdGMEY3ISIiIiIjRj4sKC0mRi82IyIiKEYwRjcqJkY/RjdGLUY3Rj4tJkYvNiMiIipGMEY3RjdGNyooLCYqJiMiIiRGOEY3RjpGN0Y3I0YnRjhGN0Y+RjVGPiwmRkZGN0ZBRj5GN0Y3">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIpNiNJInRHRipGLiwmKiYpLCYjIiIiIiM2RjQqJkYzRjQtJkkjeGNHRio2I0Y0Ri1GNCEiIiIiI0Y7LCgtJkYpNiMiIihGLUY0KiZGPEY0RidGNEY7LSZGKTYjIiIqRi1GNEY0RjQqKCwmKiYjIiIkRjVGNEY3RjRGNCNGLEY1RjRGO0YyRjssJkZDRjRGPkY7RjRGNA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiovLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJiksJiMiIiIiIzZGNyomRjZGNy0mSSN4Y0dGJTYjRjdGMEY3ISIiIiIjRj4sKC0mRi82IyIiKUYwRjcqJkY/RjdGLUY3Rj4tJkYvNiMiIzVGMEY3RjdGNyooLCYqJiNGP0Y4RjdGOkY3RjcjRidGOEY3Rj5GNUY+LCZGRkY3RkFGPkY3Rjc=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIqNiNJInRHRipGLiwmKiYpLCYjIiIiIiM2RjQqJkYzRjQtJkkjeGNHRio2I0Y0Ri1GNCEiIiIiI0Y7LCgtJkYpNiMiIilGLUY0KiZGPEY0RidGNEY7LSZGKTYjIiM1Ri1GNEY0RjQqKCwmKiYjRjxGNUY0RjdGNEY0I0YsRjVGNEY7RjJGOywmRkNGNEY+RjtGNEY0</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJiksJiMiIiIiIzZGNyomRjZGNy0mSSN4Y0dGJTYjRjdGMEY3ISIiIiIjRj4sKC0mRi82IyIiKkYwRjcqJkY/RjdGLUY3Rj5GN0Y3RjdGNyooLCZGOUY3I0YnRjhGN0Y+RjVGPiwmRjdGN0ZBRj5GN0Y3">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiM1NiNJInRHRipGLiwmKiYpLCYjIiIiIiM2RjQqJkYzRjQtJkkjeGNHRio2I0Y0Ri1GNCEiIiIiI0Y7LCgtJkYpNiMiIipGLUY0KiZGPEY0RidGNEY7RjRGNEY0RjQqKCwmRjZGNCNGLEY1RjRGO0YyRjssJkY0RjRGPkY7RjRGNA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqX:=eval(eqX);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFYRzYiLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkjeGNHRiQ2IyIiIjYjSSJ0R0YkRjAsJCooJCIrKysrK10hIzZGLiwmLSZJInVHRiQ2IyIiI0YvISIiKiYiIiVGLi0mRjlGLUYvRi5GLkYuLCYjRi4iIzZGLiomRkJGLkYqRi5GPEY8Rjw=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkjeGNHNiI2IyIiIjYjSSJ0R0YqRi4sJCooJCIrKysrK10hIzZGLCwmLSZJInVHRio2IyIiI0YtISIiKiYiIiVGLC0mRjdGK0YtRixGLEYsLCYjRiwiIzZGLComRkBGLEYnRixGOkY6Rjo=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=seq((eq[j]),j=1..N),eqX;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFzRzYiNi0vLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YkNiMiIiI2I0kidEdGJEYxLCYqJiksJiNGLyIjNkYvKiZGNkYvLSZJI3hjR0YkRi5GMEYvISIiIiIjRjwsJiomRj1GL0YrRi9GPC0mRi02I0Y9RjBGL0YvRi8qKCwmKiYjIiM1RjdGL0Y5Ri9GL0Y2Ri9GPEY1RjxGQEYvRi8vLUYoNiRGQEYxLCYqJkY0RjwsKEYrRi8qJkY9Ri9GQEYvRjwtJkYtNiMiIiRGMEYvRi9GLyooLCYqJiMiIipGN0YvRjlGL0YvI0Y9RjdGL0Y8RjVGPCwmRk9GL0YrRjxGL0YvLy1GKDYkRk9GMSwmKiZGNEY8LChGQEYvKiZGPUYvRk9GL0Y8LSZGLTYjIiIlRjBGL0YvRi8qKCwmKiYjIiIpRjdGL0Y5Ri9GLyNGUkY3Ri9GPEY1RjwsJkZbb0YvRkBGPEYvRi8vLUYoNiRGW29GMSwmKiZGNEY8LChGT0YvKiZGPUYvRltvRi9GPC0mRi02IyIiJkYwRi9GL0YvKigsJiomIyIiKEY3Ri9GOUYvRi8jRl5vRjdGL0Y8RjVGPCwmRl1wRi9GT0Y8Ri9GLy8tRig2JEZdcEYxLCYqJkY0RjwsKEZbb0YvKiZGPUYvRl1wRi9GPC0mRi02IyIiJ0YwRi9GL0YvKigsJiomI0ZicUY3Ri9GOUYvRi8jRmBwRjdGL0Y8RjVGPCwmRl9xRi9GW29GPEYvRi8vLUYoNiRGX3FGMSwmKiZGNEY8LChGXXBGLyomRj1GL0ZfcUYvRjwtJkYtNiNGZXBGMEYvRi9GLyooLCYqJkZncUYvRjlGL0YvRmZxRi9GPEY1RjwsJkZgckYvRl1wRjxGL0YvLy1GKDYkRmByRjEsJiomRjRGPCwoRl9xRi8qJkY9Ri9GYHJGL0Y8LSZGLTYjRmNvRjBGL0YvRi8qKCwmKiZGZnBGL0Y5Ri9GL0ZkcEYvRjxGNUY8LCZGXnNGL0ZfcUY8Ri9GLy8tRig2JEZec0YxLCYqJkY0RjwsKEZgckYvKiZGPUYvRl5zRi9GPC0mRi02I0ZXRjBGL0YvRi8qKCwmKiZGZG9GL0Y5Ri9GL0Zib0YvRjxGNUY8LCZGXHRGL0ZgckY8Ri9GLy8tRig2JEZcdEYxLCYqJkY0RjwsKEZec0YvKiZGPUYvRlx0Ri9GPC0mRi02I0ZHRjBGL0YvRi8qKCwmKiZGWEYvRjlGL0YvRlZGL0Y8RjVGPCwmRmp0Ri9GXnNGPEYvRi8vLUYoNiRGanRGMSwmKiZGNEY8LChGXHRGLyomRj1GL0ZqdEYvRjxGL0YvRi9GLyooLCZGOEYvRkZGL0Y8RjVGPCwmRi9GL0ZcdEY8Ri9GLy8tRig2JEY5RjEsJCooJCIrKysrK10hIzZGLywmRkBGPComRl5vRi9GK0YvRi9GL0Y1RjxGPA==">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=seq(u[i](t),i=1..N),xc[1](t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiWUc2IjYtLSZJInVHRiQ2IyIiIjYjSSJ0R0YkLSZGKDYjIiIjRistJkYoNiMiIiRGKy0mRig2IyIiJUYrLSZGKDYjIiImRistJkYoNiMiIidGKy0mRig2IyIiKEYrLSZGKDYjIiIpRistJkYoNiMiIipGKy0mRig2IyIjNUYrLSZJI3hjR0YkRilGKw==">Ni0tJkkidUc2IjYjIiIiNiNJInRHRiYtJkYlNiMiIiNGKS0mRiU2IyIiJEYpLSZGJTYjIiIlRiktJkYlNiMiIiZGKS0mRiU2IyIiJ0YpLSZGJTYjIiIoRiktJkYlNiMiIilGKS0mRiU2IyIiKkYpLSZGJTYjIiM1RiktJkkjeGNHRiZGJ0Yp</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ICs:=seq(u[i](0)=rhs(IC),i=1..N),xc[1](0)=0.999999;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkSUNzRzYiNi0vLSZJInVHRiQ2IyIiIjYjIiIhRi0vLSZGKTYjIiIjRixGLS8tJkYpNiMiIiRGLEYtLy0mRik2IyIiJUYsRi0vLSZGKTYjIiImRixGLS8tJkYpNiMiIidGLEYtLy0mRik2IyIiKEYsRi0vLSZGKTYjIiIpRixGLS8tJkYpNiMiIipGLEYtLy0mRik2IyIjNUYsRi0vLSZJI3hjR0YkRipGLCQiJyoqKioqKiEiJw==">Ni0vLSZJInVHNiI2IyIiIjYjIiIhRisvLSZGJjYjIiIjRipGKy8tJkYmNiMiIiRGKkYrLy0mRiY2IyIiJUYqRisvLSZGJjYjIiImRipGKy8tJkYmNiMiIidGKkYrLy0mRiY2IyIiKEYqRisvLSZGJjYjIiIpRipGKy8tJkYmNiMiIipGKkYrLy0mRiY2IyIjNUYqRisvLSZJI3hjR0YnRihGKiQiJyoqKioqKiEiJw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqs,ICs},{Y},type=numeric,stiff=true,abserr=1e-20,stop_cond=[u[2](t)-1,xc[1](t)],output=listprocedure);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 4432 characters]">[encoded data, 4400 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do U[i]:=subs(sol,u[i](t));od:</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U[0]:=subs(u[1](t)=U[1],u[2](t)=U[2],u[0](t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIlVHNiI2IyIiIUYn">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U[N+1]:=subs(u[N](t)=U[N],u[N-1](t)=U[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="PiZJIlVHNiI2IyIjNiIiIg==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Xc:=subs(sol,xc[1](t));</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="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol(2.);</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of 1.8213372, stop condition #2 violated</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of 1.8213372, stop condition #2 violated</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of 1.8213372, stop condition #2 violated</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of 1.8213372, stop condition #2 violated</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of 1.8213372, stop condition #2 violated</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of 1.8213372, stop condition #2 violated</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of 1.8213372, stop condition #2 violated</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of 1.8213372, stop condition #2 violated</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of 1.8213372, stop condition #2 violated</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of 1.8213372, stop condition #2 violated</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of 1.8213372, stop condition #2 violated</Text-field>
</Output>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of 1.8213372, stop condition #2 violated</Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tf:=1.8213373*0.99;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdGZHNiIkIitGUjcuPSEiKg==">JCIrRlI3Lj0hIio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(Xc(t),t=0..tf,axes=boxed,title=&quot;Figure Exp. 5.1.15.&quot;,thickness=3,labels=[t,&quot;xc&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="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pp:=plot([seq(U[i](t),i=0..N+1)],t=0..tf);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 16912 characters]">[encoded data, 16884 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display(pp,axes=boxed,title=&quot;Figure Exp. 5.2.16.&quot;,thickness=3,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, 25444 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">h:=subs(xc[1]=Xc,h);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiaEc2IiwmIyIiIiIjNkYnKiZGJkYnLUkjWGNHRiQ2I0kidEdGJEYnISIi">LCYjIiIiIiM2RiQqJkYjRiQtSSNYY0c2IjYjSSJ0R0YpRiQhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for j from 0 to 20 do p[j]:=plot([seq([evalf(subs(t=tf*j/20,Xc(t)+i*h)),evalf(subs(t=tf*j/20,U[i](t)))],i=0..N+1)]):od:</Text-field>
</Input>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({seq(p[j],j=0..20)},thickness=4,axes=boxed,title=&quot;Figure Exp. 5.2.17.&quot;,labels=[x,&quot;u&quot;]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">[encoded data, 10676 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L43" 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="L44" 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="PkkjVDFHNiI3QSQiIiFGJyQiKyE0OC8sJyEjNiQiKz1FMy03ISM1JCIrRlI3Lj1GLSQiK09fOy9DRi0kIitYbD8wSUYtJCIrYHlDMU9GLSQiK2oiKkcyVUYtJCIrdC9MM1tGLSQiKyF5ciQ0YUYtJEYpRi0kIisrV1g2bUYtJCIrMmRcN3NGLSQiKzxxYDh5Ri0kIitGJHlYVClGLSQiK0wnPmMsKkYtJCIrVjRtOycqRi0kIitELXhANSEiKiQiK2NWKD0zIkZLJCIrKFt5PjkiRkskRixGSyQiK1xuPWk3RkskIishKTNIQThGSyQiKzZdUiNRIkZLJCIrVSIqXFU5RkskIit0S2ctOkZLJCIrLnVxaTpGSyQiK006IkdpIkZLJCIrbGMiSG8iRkskIisnej5JdSJGSyRGL0ZL">N0EkIiIhRiQkIishNDgvLCchIzYkIis9RTMtNyEjNSQiK0ZSNy49RiokIitPXzsvQ0YqJCIrWGw/MElGKiQiK2B5QzFPRiokIitqIipHMlVGKiQiK3QvTDNbRiokIisheXIkNGFGKiRGJkYqJCIrK1dYNm1GKiQiKzJkXDdzRiokIis8cWA4eUYqJCIrRiR5WFQpRiokIitMJz5jLCpGKiQiK1Y0bTsnKkYqJCIrRC14QDUhIiokIitjVig9MyJGSCQiKyhbeT45IkZIJEYpRkgkIitcbj1pN0ZIJCIrISkzSEE4RkgkIis2XVIjUSJGSCQiK1UiKlxVOUZIJCIrdEtnLTpGSCQiKy51cWk6RkgkIitNOiJHaSJGSCQiK2xjIkhvIkZIJCIrJ3o+SXUiRkgkRixGSA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L45" 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="L46" 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)*L/(N+1),rhs(IC)));od:</Text-field>
</Input>
</Group>
<Group labelreference="L47" 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 M+1 do PP[i,j]:=evalf(subs(t=T1[j],U[i-1](t)));od;od:</Text-field>
</Input>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plotdata := [seq([ seq([eval(subs(t=T1[j],Xc(t)+(i-1)*h)),T1[j],PP[i,j]], i=1..N+2)], j=1..M+1)]:</Text-field>
</Input>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">surfdata(plotdata,axes=boxed,title=&quot;Figure Exp. 5.2.18.&quot;, labels=[x,t,u],orientation=[-90,0]);</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, 18120 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>