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<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 3.2.2  Series Solutions for Non-isothermal Catalyst Pellet - Multiple Steady States</Font></Text-field>
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<Text-field style="Text" layout="Normal">The dimensionless concentration in a non-isothermal catalyst pellet<Font superscript="true">[8]</Font> is governed by:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="Text" input-equation="" display="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">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</Equation></Text-field>
<Text-field style="Text" layout="Normal">with the boundary conditions:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
<Text-field style="Text" layout="Normal">and</Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">This boundary value problem  has multiple solutions for \316\246=0.2, \316\262=0.8 and \316\263=20.  The series solutions are obtained for this problem in Maple below:</Font></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots):</Text-field>
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<Text-field style="Text" layout="Normal">The governing equation is entered here:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=diff(c(x),x$2)=Phi^2*c(x)*exp(gamma*beta*(1-c(x))/(1+beta*(1-c(x))));</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JImNHRiQ2I0kieEdGJC1JIiRHRig2JEYtIiIjKigpSSRQaGlHRiRGMSIiIkYqRjUtSSRleHBHNiRGKEkoX3N5c2xpYkdGJDYjKipJJmdhbW1hR0YoRjVJJWJldGFHRiRGNSwmRjVGNUYqISIiRjUsJkY1RjUqJkY9RjVGPkY1RjVGP0Y1">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC1JImNHNiI2I0kieEdGK0YtRi0qKEkkUGhpR0YrIiIjRikiIiItSSRleHBHNiRGJUkoX3N5c2xpYkdGKzYjKipJJmdhbW1hR0YlRjFJJWJldGFHRitGMSwmRjFGMUYpISIiRjEsJkYxRjEqJkY5RjFGOkYxRjFGO0Yx</Equation></Text-field>
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<Text-field style="Text" layout="Normal">The values for the parameters are entered here:</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=subs(gamma=20,beta=0.8,eq);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JImNHRiQ2I0kieEdGJC1JIiRHRig2JEYtIiIjKigpSSRQaGlHRiRGMSIiIkYqRjUtSSRleHBHNiRGKEkoX3N5c2xpYkdGJDYjLCQqKCQiJGciISIiRjUsJkY1RjVGKkY/RjUsJiQiIz1GP0Y1KiYkIiIpRj9GNUYqRjVGP0Y/RjVGNQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC1JImNHNiI2I0kieEdGK0YtRi0qKEkkUGhpR0YrIiIjRikiIiItSSRleHBHNiRGJUkoX3N5c2xpYkdGKzYjLCQqJiwmRjFGMUYpISIiRjEsJiQiIz1GOkYxRikkISIpRjpGOiQiJGciRjpGMQ==</Equation></Text-field>
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<Text-field style="Text" layout="Normal">The boundary condition at x=1 is entered here:</Text-field>
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<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc:=c(x)-1;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjYmNHNiIsJi1JImNHRiQ2I0kieEdGJCIiIkYqISIi">LCYtSSJjRzYiNiNJInhHRiUiIiIhIiJGKA==</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">The order of the series solution is specified and the governing equation is solved as a function of c1, the concentration at the center, and \316\246:</Font></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Order:=8;</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmT3JkZXJHNiIiIik=">IiIp</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eq,c(0)=c1,D(c)(0)=0},{c(x)},type=series);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkkc29sRzYiLy1JImNHRiQ2I0kieEdGJCstRilJI2MxR0YkIiIhLCQqKiMiIiIiIiNGMClJJFBoaUdGJEYxRjBGK0YwLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJCooIiMhKUYwLCZGMCEiIkYrRjBGMCwmIiIqRj4qJiIiJUYwRitGMEYwRj5GMEYwRjBGMSwkKi4jRjAiI0NGMClGM0ZCRjApRjRGMUYwRitGMCwoIiMiKUYwKiYiJHMlRjBGK0YwRj4qJiIjO0YwKUYrRjFGMEYwRjApRj9GMUY+RjBGQiwkKi4jRjAiJD8oRjApRjMiIidGMEYrRjApRjQiIiRGMCwsKiYiJ2szRkYwRitGMEY+KiYiJ3c8ekYwRk9GMEYwKiYiJi9eIkYwKUYrRlhGMEY+IiVobEYwKiYiJGMjRjApRitGQkYwRjBGMClGP0ZCRj5GMEZWLUkiT0dGNzYjRjAiIik=">Ly1JImNHNiI2I0kieEdGJSstRidJI2MxR0YlIiIhLCQqKEkkUGhpR0YlIiIjRikiIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IywkKiYsJiEiIkYvRilGL0YvLCYhIipGL0YpIiIlRjkiIyEpRi8jRi9GLkYuLCQqLEYtRjxGMEYuRilGLywoIiMiKUYvRikhJHMlKiRGKUYuIiM7Ri9GOiEiIyNGLyIjQ0Y8LCQqLEYtIiInRilGL0YwIiIkLCxGKSEnazNGRkQiJ3c8eiokRilGTCEmL14iIiVobEYvKiRGKUY8IiRjI0YvRjohIiUjRi8iJD8oRkstSSJPR0YzNiNGLyIiKQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L54" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The series solution obtained is stored in ca:</Text-field>
</Input>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ca:=convert(rhs(sol),polynom);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjY2FHNiIsKkkjYzFHRiQiIiIqLCNGJyIiI0YnKUkkUGhpR0YkRipGJ0YmRictSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKigiIyEpRicsJkYnISIiRiZGJ0YnLCYiIipGNyomIiIlRidGJkYnRidGN0YnRicpSSJ4R0YkRipGJ0YnKjAjRiciI0NGJylGLEY7RicpRi1GKkYnRiZGJywoIiMiKUYnKiYiJHMlRidGJkYnRjcqJiIjO0YnKUYmRipGJ0YnRicpRjhGKkY3KUY9RjtGJ0YnKjAjRiciJD8oRicpRiwiIidGJ0YmRicpRi0iIiRGJywsKiYiJ2szRkYnRiZGJ0Y3KiYiJ3c8ekYnRklGJ0YnKiYiJi9eIkYnKUYmRlJGJ0Y3IiVobEYnKiYiJGMjRicpRiZGO0YnRidGJylGOEY7RjcpRj1GUEYnRic=">LCpJI2MxRzYiIiIiKipJJFBoaUdGJCIiI0YjRiUtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiYsJiEiIkYlRiNGJUYlLCYhIipGJUYjIiIlRjIiIyEpRiVJInhHRiRGKCNGJUYoKi5GJ0Y1RilGKEYjRiUsKCIjIilGJUYjISRzJSokRiNGKCIjO0YlRjMhIiNGN0Y1I0YlIiNDKi5GJyIiJ0YjRiVGKSIiJCwsRiMhJ2szRkY9Iid3PHoqJEYjRkQhJi9eIiIlaGxGJSokRiNGNSIkYyNGJUYzISIlRjdGQyNGJSIkPyg=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The boundary condition at x=1 is evaluated using the series solution obtained:</Text-field>
</Input>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqc:=subs(c(x)=ca,bc);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFjRzYiLCxJI2MxR0YkIiIiKiwjRiciIiNGJylJJFBoaUdGJEYqRidGJkYnLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJCooIiMhKUYnLCZGJyEiIkYmRidGJywmIiIqRjcqJiIiJUYnRiZGJ0YnRjdGJ0YnKUkieEdGJEYqRidGJyowI0YnIiNDRicpRixGO0YnKUYtRipGJ0YmRicsKCIjIilGJyomIiRzJUYnRiZGJ0Y3KiYiIztGJylGJkYqRidGJ0YnKUY4RipGNylGPUY7RidGJyowI0YnIiQ/KEYnKUYsIiInRidGJkYnKUYtIiIkRicsLComIidrM0ZGJ0YmRidGNyomIid3PHpGJ0ZJRidGJyomIiYvXiJGJylGJkZSRidGNyIlaGxGJyomIiRjI0YnKUYmRjtGJ0YnRicpRjhGO0Y3KUY9RlBGJ0YnRidGNw==">LCxJI2MxRzYiIiIiKipJJFBoaUdGJCIiI0YjRiUtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiYsJiEiIkYlRiNGJUYlLCYhIipGJUYjIiIlRjIiIyEpRiVJInhHRiRGKCNGJUYoKi5GJ0Y1RilGKEYjRiUsKCIjIilGJUYjISRzJSokRiNGKCIjO0YlRjMhIiNGN0Y1I0YlIiNDKi5GJyIiJ0YjRiVGKSIiJCwsRiMhJ2szRkY9Iid3PHoqJEYjRkQhJi9eIiIlaGxGJSokRiNGNSIkYyNGJUYzISIlRjdGQyNGJSIkPyhGMkYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqc:=subs(x=1,eqc);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFjRzYiLCxJI2MxR0YkIiIiKiojRiciIiNGJylJJFBoaUdGJEYqRidGJkYnLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJCooIiMhKUYnLCZGJyEiIkYmRidGJywmIiIqRjcqJiIiJUYnRiZGJ0YnRjdGJ0YnRicqLiNGJyIjQ0YnKUYsRjtGJylGLUYqRidGJkYnLCgiIyIpRicqJiIkcyVGJ0YmRidGNyomIiM7RicpRiZGKkYnRidGJylGOEYqRjdGJyouI0YnIiQ/KEYnKUYsIiInRidGJkYnKUYtIiIkRicsLComIidrM0ZGJ0YmRidGNyomIid3PHpGJ0ZHRidGJyomIiYvXiJGJylGJkZPRidGNyIlaGxGJyomIiRjI0YnKUYmRjtGJ0YnRicpRjhGO0Y3RidGJ0Y3">LCxJI2MxRzYiIiIiKihJJFBoaUdGJCIiI0YjRiUtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiYsJiEiIkYlRiNGJUYlLCYhIipGJUYjIiIlRjIiIyEpRiUjRiVGKCosRidGNUYpRihGI0YlLCgiIyIpRiVGIyEkcyUqJEYjRigiIztGJUYzISIjI0YlIiNDKixGJyIiJ0YjRiVGKSIiJCwsRiMhJ2szRkY8Iid3PHoqJEYjRkMhJi9eIiIlaGxGJSokRiNGNSIkYyNGJUYzISIlI0YlIiQ/KEYyRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The equation for c1 is plotted as a function of c1.  We observe that there are four solutions:</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(subs(Phi=0.2,eqc),c1=0..1,view=[0..1,-1..1],title=&quot;Figure Exp. 3.2.2.&quot;,thickness=4);</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, 4520 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The values for the constant c1 are obtained using the 'fsolve' command.</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cc[1]:=fsolve(subs(Phi=0.2,eqc),c1=1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2NjRzYiNiMiIiIkIitoOiZvciohIzU=">JCIraDomb3IqISM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cc[2]:=fsolve(subs(Phi=0.2,eqc),c1=0.8);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2NjRzYiNiMiIiMkIittUXZ6ISkhIzU=">JCIrbVF2eiEpISM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cc[3]:=fsolve(subs(Phi=0.2,eqc),c1=0.0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2NjRzYiNiMiIiQkIitqVGFuRSEjOQ==">JCIralRhbkUhIzk=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cc[4]:=fsolve(subs(Phi=0.2,eqc),c1=0.03);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2NjRzYiNiMiIiUkIitJdGY5SCEjNg==">JCIrSXRmOUghIzY=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">We obtain four different solutions for c1.  These values for c1 and \316\246 are substituted in the series solution obtained and plots are made:</Font></Text-field>
</Input>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p1:=plot(subs(c1=cc[1],Phi=0.2,ca),x=0..1,thickness=4,color=black,axes=boxed):</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p2:=plot(subs(c1=cc[2],Phi=0.2,ca),x=0..1,thickness=4,color=blue,axes=boxed):</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p3:=plot(subs(c1=cc[3],Phi=0.2,ca),x=0..1,thickness=4,color=brown,axes=boxed):</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p4:=plot(subs(c1=cc[4],Phi=0.2,ca),x=0..1,thickness=4,color=red,axes=boxed):</Text-field>
</Input>
</Group>
<Group labelreference="L63" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pt:=textplot([[0.3,evalf(subs(x=0.3,c1=cc[1],Phi=0.2,ca)+0.04),[c1=cc[1],Phi=0.2]],[0.3,evalf(subs(x=0.3,c1=cc[2],Phi=0.2,ca)+0.04),[c1=cc[2],Phi=0.2]],[0.3,evalf(subs(x=0.3,c1=cc[3],Phi=0.2,ca)+0.04),[c1=cc[3],Phi=0.2]]]):</Text-field>
</Input>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({p1,p2,p3,pt},title=&quot;Figure Exp. 3.2.3.&quot;,labels=[x,c],view=[0..1,-0.01..1.05]);</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, 33788 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display(p4,labels=[x,c],title=&quot;Figure Exp. 3.2.4.&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">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We observe that the first three values of c1 make sense and we discard the fourth value.  There is no guarantee that the solution obtained is the converged one.  The accuracy and convergence of the series solution are analyzed below by increasing the number of terms in the series.</Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Order:=16;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmT3JkZXJHNiIiIzs=">IiM7</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eq,c(0)=c1,D(c)(0)=0},{c(x)},type=series):</Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ca:=convert(rhs(sol),polynom):</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqc:=subs(c(x)=ca,bc):</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqc:=subs(x=1,eqc):</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cc2[1]:=fsolve(subs(Phi=0.2,eqc),c1=1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJGNjMkc2IjYjIiIiJCIrZ0tBPCgqISM1">JCIrZ0tBPCgqISM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cc2[2]:=fsolve(subs(Phi=0.2,eqc),c1=0.8);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJGNjMkc2IjYjIiIjJCIrKnpDUyp5ISM1">JCIrKnpDUyp5ISM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cc2[3]:=fsolve(subs(Phi=0.2,eqc),c1=0.0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJGNjMkc2IjYjIiIkJCIrOSMpcC5EISM7">JCIrOSMpcC5EISM7</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to 3 do print(cc[i],cc2[i]);od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiQkIitoOiZvciohIzUkIitnS0E8KCpGJQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiQkIittUXZ6ISkhIzUkIisqekNTKnlGJQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiQkIitqVGFuRSEjOSQiKzkjKXAuRCEjOw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We observe that the first value for c1 has converged (3-digit accuracy).  The second value of c1 has converged to two digit accuracy.  The third value has not converged yet.  But the order of magnitude for the third value of c1 has converged.  Next, plots are made for three different values of c1.</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Order:=20;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmT3JkZXJHNiIiIz8=">IiM/</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eq,c(0)=c1,D(c)(0)=0},{c(x)},type=series):</Text-field>
</Input>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ca:=convert(rhs(sol),polynom):</Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqc:=subs(c(x)=ca,bc):</Text-field>
</Input>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqc:=subs(x=1,eqc):</Text-field>
</Input>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cc3[1]:=fsolve(subs(Phi=0.2,eqc),c1=1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJGNjM0c2IjYjIiIiJCIrTUxBPCgqISM1">JCIrTUxBPCgqISM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cc3[2]:=fsolve(subs(Phi=0.2,eqc),c1=0.8);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJGNjM0c2IjYjIiIjJCIrW086VXkhIzU=">JCIrW086VXkhIzU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cc3[3]:=fsolve(subs(Phi=0.2,eqc),c1=0.0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJGNjM0c2IjYjIiIkJCIrejRQazYhIzs=">JCIrejRQazYhIzs=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to 3 do print(cc[i],cc2[i],cc3[i]);od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiUkIitoOiZvciohIzUkIitnS0E8KCpGJSQiK01MQTwoKkYl</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiUkIittUXZ6ISkhIzUkIisqekNTKnlGJSQiK1tPOlV5RiU=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiUkIitqVGFuRSEjOSQiKzkjKXAuRCEjOyQiK3o0UGs2Rig=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We observe that the first value for c1 has converged (3-digit accuracy).  The second value of c1 has converged to two digits accuracy.  The third value has not converged yet.  But, the order of magnitude for the third value of c1 has converged.  Next, plots are made for three different values of c1.</Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p1:=plot(subs(c1=cc3[1],Phi=0.2,ca),x=0..1,thickness=4,color=black,axes=boxed):</Text-field>
</Input>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p2:=plot(subs(c1=cc3[2],Phi=0.2,ca),x=0..1,thickness=4,color=blue,axes=boxed):</Text-field>
</Input>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p3:=plot(subs(c1=cc3[3],Phi=0.2,ca),x=0..1,thickness=4,color=brown,axes=boxed):</Text-field>
</Input>
</Group>
<Group labelreference="L67" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pt:=textplot([[0.3,evalf(subs(x=0.3,c1=cc3[1],Phi=0.2,ca)+0.04),[c1=cc3[1],Phi=0.2]],[0.3,evalf(subs(x=0.3,c1=cc3[2],Phi=0.2,ca)+0.04),[c1=cc3[2],Phi=0.2]],[0.3,evalf(subs(x=0.3,c1=cc3[3],Phi=0.2,ca)+0.04),[c1=cc3[3],Phi=0.2]]]):</Text-field>
</Input>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({p1,p2,p3,pt},labels=[x,c],title=&quot;Figure Exp. 3.2.5.&quot;,view=[0..1,-0.01..1.05]);</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>
</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, 33788 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Multiple steady states in a rectangular catalyst pellet were analyzed in this example.  This problem will be revisited later in this chapter.</Text-field>
</Input>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>