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<Input>
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 2.2.2</Font></Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Consider an n<Font superscript="true">th</Font> order reaction</Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><Image height="35" width="181" zoomable="false">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</Image></Text-field>
<Text-field style="Text" layout="Normal">governed by the ODE:</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="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkmbWZyYWNHRiQ2KC1GIzYlLUkjbW9HRiQ2LVEwJkRpZmZlcmVudGlhbEQ7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZ1bnNldEYnLyUqc2VwYXJhdG9yR0Y5LyUpc3RyZXRjaHlHRjkvJSpzeW1tZXRyaWNHRjkvJShsYXJnZW9wR0Y5LyUubW92YWJsZWxpbWl0c0dGOS8lJ2FjY2VudEdGOS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkgtSSNtaUdGJDYlUSJjRicvJSdpdGFsaWNHUSZmYWxzZUYnRjRGNC1GIzYmRjAtRjE2LVEifkYnRjQvRjhGUS9GO0ZRL0Y9RlEvRj9GUS9GQUZRL0ZDRlEvRkVGUUZGRkktRkw2JVEidEYnRk9GNEY0LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zgby8lKWJldmVsbGVkR0ZRLUYxNi1RIj1GJ0Y0RldGWEZZRlpGZW5GZm5GZ24vRkdRLDAuMjc3Nzc3OGVtRicvRkpGaW9GVC1GMTYtUSomdW1pbnVzMDtGJ0Y0RldGWEZZRlpGZW5GZm5GZ24vRkdRLDAuMjIyMjIyMmVtRicvRkpGX3BGVC1GTDYlUSNrY0YnRk9GNC1GTDYnUSJuRicvJSVzaXplR1EjMTBGJ0ZPLyUsc3VwZXJzY3JpcHRHUSV0cnVlRidGNEY0">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</Equation></Text-field>
<Text-field style="Text" layout="Normal">with the initial conditions c(0)=1; k is the rate constant , and n is the order of the reaction.  Series solutions are obtained in Maple below:</Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
</Group>
<Group labelreference="L3" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the governing equation:</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=diff(c(t),t)=-k*c(t)^n;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JImNHRiQ2I0kidEdGJEYtLCQqJkkia0dGJCIiIilGKkkibkdGJEYxISIi">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJjRzYiNiNJInRHRilGKywkKiZJImtHRikiIiIpRidJIm5HRilGLyEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The analytical solution is found as:</Text-field>
</Input>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ca:=rhs(dsolve({eq,c(0)=1},c(t)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjY2FHNiIqJCksKComSSJrR0YkIiIiSSJ0R0YkRiohIiIqKEYpRipGK0YqSSJuR0YkRipGKkYqRioqJCwmRi5GKkYqRixGLEYs">KiQpLCgqJkkia0c2IiIiIkkidEdGJ0YoISIiKihGJkYoRilGKEkibkdGJ0YoRihGKEYoKiQsJkYsRihGKkYoRipGKg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, the series solution can be obtained as:</Text-field>
</Input>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eq,c(0)=1},{c(t)},type=series);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkkc29sRzYiLy1JImNHRiQ2I0kidEdGJCsxRikiIiIiIiEsJEkia0dGJCEiIkYrLCQqKCNGKyIiI0YrKUYuRjNGK0kibkdGJEYrRitGMywmKigjRisiIiRGKylGLkY5RispRjVGM0YrRi8qKCNGKyIiJ0YrRjpGK0Y1RitGK0Y5LCQqKiNGKyIjQ0YrKUYuIiIlRitGNUYrLCgqJkY+RitGO0YrRisqJiIiKEYrRjVGK0YvRjNGK0YrRitGRCwqKigjRisiIiZGKylGLkZMRispRjVGREYrRi8qKCMiI0IiI2dGK0ZNRispRjVGOUYrRisqKCMiI0giJD8iRitGTUYrRjtGK0YvKigjRisiIz9GK0ZNRitGNUYrRitGTC1JIk9HJSpwcm90ZWN0ZWRHNiNGK0Y+">Ly1JImNHNiI2I0kidEdGJSsxRiciIiIiIiEsJEkia0dGJSEiIkYpLCQqJkYsIiIjSSJuR0YlRikjRilGMEYwLCYqJkYsIiIkRjFGMCNGLUY1KiZGLEY1RjFGKSNGKSIiJ0Y1LCQqKEYsIiIlRjFGKSwoKiRGMUYwRjlGMSEiKEYwRilGKSNGKSIjQ0Y8LCoqJkYsIiImRjFGPCNGLUZEKiZGLEZERjFGNSMiI0IiI2cqJkYsRkRGMUYwIyEjSCIkPyIqJkYsRkRGMUYpI0YpIiM/RkQtSSJPRyUqcHJvdGVjdGVkRzYjRilGOQ==</Equation></Text-field>
</Output>
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<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">By default, Maple returns series solutions accurate to the order of t<Font superscript="true">6</Font> .  The order can be increased as:</Text-field>
</Input>
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<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Order:=8;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmT3JkZXJHNiIiIik=">IiIp</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eq,c(0)=1},{c(t)},type=series);</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="L37" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The order obtained is converted to polynomial form for plotting purposes.</Text-field>
</Input>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">assign(sol):</Text-field>
</Input>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">c(t):=convert(c(t),polynom);</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="L38" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, the series solution obtained is plotted for different values of parameters and compared with the analytical solution.</Text-field>
</Input>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={k=1,n=1};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwkL0kibkdGJCIiIi9JImtHRiRGKA==">PCQvSSJuRzYiIiIiL0kia0dGJUYm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">C:=subs(pars,c(t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQ0c2IiwyIiIiRiZJInRHRiQhIiIqJiNGJiIiI0YmKUYnRitGJkYmKiYjRiYiIidGJilGJyIiJEYmRigqJiNGJiIjQ0YmKUYnIiIlRiZGJiomI0YmIiQ/IkYmKUYnIiImRiZGKComI0YmIiQ/KEYmKUYnRi9GJkYmKiYjRiYiJVNdRiYpRiciIihGJkYo">LDIiIiJGI0kidEc2IiEiIiokRiQiIiMjRiNGKCokRiQiIiQjRiYiIicqJEYkIiIlI0YjIiNDKiRGJCIiJiNGJiIkPyIqJEYkRi0jRiMiJD8oKiRGJCIiKCNGJiIlU10=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=subs(pars,ca);</Text-field>
</Input>
<Output>
<Text-field style="Error" layout="Error">Error, numeric exception: division by zero</Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Since division by zero occurs, the limit is obtained.</Text-field>
</Input>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=limit(ca,n=1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjQ2FHNiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiZJImtHRiQiIiJJInRHRiRGLiEiIg==">LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComSSJrR0YnIiIiSSJ0R0YnRiwhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=subs(k=1,Ca);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjQ2FHNiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkSSJ0R0YkISIi">LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJEkidEdGJyEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tf:=3;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdGZHNiIiIiQ=">IiIk</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([C,Ca],t=0..tf,thickness=4,axes=boxed,title=&quot;Figure Exp. 2.2.3&quot;,labels=[t,&quot;C&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, 5180 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We observe that the series solution diverges for values of t greater than 2.  Next, plots are made for different values of the parameters:</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={k=1,n=1/3};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwkL0kia0dGJCIiIi9JIm5HRiQjRigiIiQ=">PCQvSSJrRzYiIiIiL0kibkdGJSNGJiIiJA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">C:=subs(pars,c(t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQ0c2IiwyIiIiRiZJInRHRiQhIiIqJiNGJiIiJ0YmKUYnIiIjRiZGJiomI0YmIiNhRiYpRiciIiRGJkYmKiYjRiYiJDsjRiYpRiciIiVGJkYmKiYjRiYiJFsnRiYpRiciIiZGJkYmKiYjIiIoIiZrOyJGJilGJ0YrRiZGJiomI0YmIiUpKVFGJilGJ0Y/RiZGJg==">LDIiIiJGI0kidEc2IiEiIiokRiQiIiMjRiMiIicqJEYkIiIkI0YjIiNhKiRGJCIiJSNGIyIkOyMqJEYkIiImI0YjIiRbJyokRiRGKiMiIigiJms7IiokRiRGOSNGIyIlKSlR</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=subs(pars,ca);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjQ2FHNiIqJCksJiomIyIiIyIiJCIiIkkidEdGJEYsISIiRixGLCNGK0YqRiw=">KiQsJkkidEc2IiMhIiMiIiQiIiJGKSNGKCIiIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tf:=1.5;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdGZHNiIkIiM6ISIi">JCIjOiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([C,Ca],t=0..tf,thickness=4,axes=boxed,title=&quot;Figure Exp. 2.2.4&quot;,labels=[t,&quot;C&quot;]);</Text-field>
<Text-field style="Normal" layout="Normal"></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, 5204 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">For these values, both the exact analytical solution and the series solution match exactly until t=1.4.  Next, a second order reaction is considered.</Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={k=1,n=2};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwkL0kia0dGJCIiIi9JIm5HRiQiIiM=">PCQvSSJrRzYiIiIiL0kibkdGJSIiIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">C:=subs(pars,c(t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQ0c2IiwyIiIiRiZJInRHRiQhIiIqJClGJyIiI0YmRiYqJClGJyIiJEYmRigqJClGJyIiJUYmRiYqJClGJyIiJkYmRigqJClGJyIiJ0YmRiYqJClGJyIiKEYmRig=">LDIiIiJGI0kidEc2IiEiIiokRiQiIiNGIyokRiQiIiRGJiokRiQiIiVGIyokRiQiIiZGJiokRiQiIidGIyokRiQiIihGJg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=subs(pars,ca);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjQ2FHNiIqJCwmSSJ0R0YkIiIiRihGKCEiIg==">KiQsJkkidEc2IiIiIkYmRiYhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" 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="PkkjdGZHNiIiIiI=">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([C,Ca],t=0..tf,thickness=4,axes=boxed,title=&quot;Figure 2.2.5&quot;,labels=[t,&quot;C&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, 5384 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">For this case, the series solution starts to diverge after t is greater than 0.4.  Hence, one has to be careful while using series solutions.  The divergence of the series solution obtained depends upon the problem and values of the parameters.  Nevertheless, Maple can give series solutions to the order t<Font superscript="true">100</Font> also.</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>