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    </Task-category>
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    <Annotation-category name="&lt;default&gt;">
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<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 2.2.6 Stiff Ordinary Differential Equations</Font></Text-field>
</Input>
</Group>
<Group labelreference="L20" 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(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The governing equations are entered here:</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[1]:=diff(B(t),t)=k*B(t)*S(t)/(K+S(t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JIkJHRiU2I0kidEdGJUYwKipJImtHRiVGJ0YtRictSSJTR0YlRi9GJywmSSJLR0YlRidGM0YnISIi">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJCRzYiNiNJInRHRilGKyoqSSJrR0YpIiIiRidGLi1JIlNHRilGKkYuLCZJIktHRilGLkYvRi4hIiI=</Equation></Text-field>
</Output>
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<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[2]:=diff(S(t),t)=-0.75*k*B(t)*S(t)/(K+S(t));;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JIlNHRiU2I0kidEdGJUYwLCQqLCQiI3YhIiMiIiJJImtHRiVGNi1JIkJHRiVGL0Y2Ri1GNiwmSSJLR0YlRjZGLUY2ISIiRjw=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJTRzYiNiNJInRHRilGKywkKipJImtHRikiIiItSSJCR0YpRipGL0YnRi8sJkkiS0dGKUYvRidGLyEiIiQhI3YhIiM=</Equation></Text-field>
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<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation>The dependent variables are entered here:</Text-field>
</Input>
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<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=(B(t),S(t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkldmFyc0c2IjYkLUkiQkdGJDYjSSJ0R0YkLUkiU0dGJEYo">NiQtSSJCRzYiNiNJInRHRiUtSSJTR0YlRiY=</Equation></Text-field>
</Output>
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<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The parameters are entered here:</Text-field>
</Input>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={k=0.3,K=1e-6};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwkL0kia0dGJCQiIiQhIiIvSSJLR0YkJCIiIiEiJw==">PCQvSSJrRzYiJCIiJCEiIi9JIktHRiUkIiIiISIn</Equation></Text-field>
</Output>
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<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=(subs(pars,eq[1]),subs(pars,eq[2]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFzRzYiNiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JIkJHRiQ2I0kidEdGJEYuLCQqKiQiIiQhIiIiIiJGK0Y0LUkiU0dGJEYtRjQsJiRGNCEiJ0Y0RjVGNEYzRjQvLUYoNiRGNUYuLCQqKiQiJEQjISIkRjRGK0Y0RjVGNEY3RjNGMw==">NiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JIkJHNiI2I0kidEdGKkYsLCQqKEYoIiIiLUkiU0dGKkYrRi8sJiRGLyEiJ0YvRjBGLyEiIiQiIiRGNS8tRiU2JEYwRiwsJEYuJCEkRCMhIiQ=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The initial conditions are entered here:</Text-field>
</Input>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ICs:=(B(0)=0.05,S(0)=5);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkSUNzRzYiNiQvLUkiQkdGJDYjIiIhJCIiJiEiIy8tSSJTR0YkRilGLA==">NiQvLUkiQkc2IjYjIiIhJCIiJiEiIy8tSSJTR0YmRidGKg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, the numerical solution is found and plotted until t=20:</Text-field>
</Input>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqs,ICs},{vars},type=numeric);</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="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tf:=20;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdGZHNiIiIz8=">IiM/</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[t,B(t)],0..tf,title=&quot;Figure Exp. 2.2.14&quot;,color=red,axes=boxed,thickness=3);</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="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[t,S(t)],0..tf,title=&quot;Figure Exp. 2.2.15&quot;,color=green,axes=boxed,thickness=3);</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="L30" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We observe that Maple predicts negative concentration.  This is because the default absolute error in 'dsolve' numeric is only 1d-6, which can be decreased to predict more accurate solutions:</Text-field>
</Input>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqs,ICs},{vars},type=numeric,abserr=1e-10);</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="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[t,B(t)],0..tf,title=&quot;Figure Exp. 2.2.16&quot;,axes=boxed,color=gold,thickness=3);</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of 16.734694, maxfun limit exceeded (see ?dsolve,maxfun for details)</Text-field>
</Output>
<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="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[t,S(t)],0..tf,title=&quot;Figure Exp. 2.2.17&quot;,color=gold,axes=boxed,thickness=3);</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of 16.734694, maxfun limit exceeded (see ?dsolve,maxfun for details)</Text-field>
</Output>
<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>
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<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Maple's default Runge-Kutta method cannot predict the profiles after T=16.3.  In addition, the program takes too long to run.  This is a still problem and can be conveniently solved by using Maple's still solver.</Text-field>
</Input>
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<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqs,ICs},{vars},type=numeric,stiff=true,abserr=1e-10);</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>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[t,B(t)],0..tf,title=&quot;Figure Exp. 2.2.18&quot;, color=brown,axes=boxed,thickness=3);</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>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[t,S(t)],0..tf,title=&quot;Figure Exp. 2.2.19&quot;,color=black,axes=boxed,thickness=3);</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"></Text-field>
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<Output>
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<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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</Worksheet>