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<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 2.2.3b  Diffusion with a Second Order Reaction</Font></Text-field>
</Input>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Example 3.2.1 is solved using finite differences in Maple below.  The program developed for example 3.8 is modified to solve this example.  (Note that y is used as the dependent variable instead of c.)</Text-field>
</Input>
</Group>
<Group labelreference="L33" 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="L35" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The number of node points is entered here:</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=10;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTkc2IiIjNQ==">IiM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The length of the domain is entered here:</Text-field>
</Input>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">L:=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTEc2IiIiIg==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The governing equation is entered below:</Text-field>
</Input>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=diff(y(x),x$2)-Phi^2*y(x)^2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIsJi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ5R0YkNiNJInhHRiQtSSIkR0YoNiRGLSIiIyIiIiomKUkkUGhpR0YkRjFGMilGKkYxRjIhIiI=">LCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYkNiQtSSJ5RzYiNiNJInhHRitGLUYtIiIiKiYpSSRQaGlHRisiIiNGLilGKUYyRi4hIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The boundary conditions are entered here:</Text-field>
</Input>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=diff(y(x),x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiQ2I0kieEdGJEYs">LUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHNiI2I0kieEdGKEYq</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=y(x)-1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLCYtSSJ5R0YkNiNJInhHRiQiIiJGKiEiIg==">LCYtSSJ5RzYiNiNJInhHRiUiIiJGKCEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Next, a general program is written to convert the governing equation and the boundary conditions to finite difference form.  The central difference expression for the second and first derivatives are:</Text-field>
</Input>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">d2ydx2:=(y[m+1]-2*y[m]+y[m-1])/h^2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknZDJ5ZHgyRzYiKiYsKCZJInlHRiQ2IywmSSJtR0YkIiIiRixGLEYsKiYiIiNGLCZGKDYjRitGLCEiIiZGKDYjLCZGK0YsRixGMUYsRiwpSSJoR0YkRi5GMQ==">KiYsKCZJInlHNiI2IywmSSJtR0YmIiIiRipGKkYqKiYiIiNGKiZGJTYjRilGKiEiIiZGJTYjLCZGKUYqRipGL0YqRiopSSJoR0YmRixGLw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydx:=(y[m+1]-y[m-1])/2/h;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklZHlkeEc2IiwkKigjIiIiIiIjRigsJiZJInlHRiQ2IywmSSJtR0YkRihGKEYoRigmRiw2IywmRi9GKEYoISIiRjNGKEkiaEdGJEYzRig=">LCQqKCMiIiIiIiNGJSwmJkkieUc2IjYjLCZJIm1HRipGJUYlRiVGJSZGKTYjLCZGLUYlRiUhIiJGMUYlSSJoR0YqRjFGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> Three point forward and backward difference expressions for the derivative are:</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxf:=(-y[2]+4*y[1]-3*y[0])/(2*h);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGZHNiIsJCooIyIiIiIiI0YoLCgmSSJ5R0YkNiNGKSEiIiomIiIlRigmRiw2I0YoRihGKComIiIkRigmRiw2IyIiIUYoRi5GKEkiaEdGJEYuRig=">LCQqKCMiIiIiIiNGJSwoJkkieUc2IjYjRiYhIiIqJiIiJUYlJkYpNiNGJUYlRiUqJiIiJEYlJkYpNiMiIiFGJUYsRiVJImhHRipGLEYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxb:=(y[N-1]-4*y[N]+3*y[N+1])/(2*h);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGJHNiIsJCooIyIiIiIiI0YoLCgmSSJ5R0YkNiMiIipGKComIiIlRigmRiw2IyIjNUYoISIiKiYiIiRGKCZGLDYjIiM2RihGKEYoSSJoR0YkRjRGKA==">LCQqKCMiIiIiIiNGJSwoJkkieUc2IjYjIiIqRiUqJiIiJUYlJkYpNiMiIzVGJSEiIiomIiIkRiUmRik2IyIjNkYlRiVGJUkiaEdGKkYyRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> The governing equation in finite difference form is:</Text-field>
</Input>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq[m]:=subs(diff(y(x),x$2)=d2ydx2,diff(y(x),x)=dydx,y(x)=y[m],x=m*h,eq);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiNJIm1HRiUsJiomLCgmSSJ5R0YlNiMsJkYnIiIiRi9GL0YvKiYiIiNGLyZGLEYmRi8hIiImRiw2IywmRidGL0YvRjNGL0YvKUkiaEdGJUYxRjNGLyomKUkkUGhpR0YlRjFGLylGMkYxRi9GMw==">LCYqJiwoJkkieUc2IjYjLCZJIm1HRiciIiJGK0YrRisqJiIiI0YrJkYmNiNGKkYrISIiJkYmNiMsJkYqRitGK0YwRitGKylJImhHRidGLUYwRisqJilJJFBoaUdGJ0YtRispRi5GLUYrRjA=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> The boundary conditions in finite difference form are:</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq[0]:=subs(diff(y(x),x)=dydxf,y(x)=y[0],bc1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiEsJCooIyIiIiIiI0YrLCgmSSJ5R0YlNiNGLCEiIiomIiIlRismRi82I0YrRitGKyomIiIkRismRi9GJkYrRjFGK0kiaEdGJUYxRis=">LCQqKCMiIiIiIiNGJSwoJkkieUc2IjYjRiYhIiIqJiIiJUYlJkYpNiNGJUYlRiUqJiIiJEYlJkYpNiMiIiFGJUYsRiVJImhHRipGLEYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq[N+1]:=subs(diff(y(x),x)=dydxb,y(x)=y[N+1],bc2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzYsJiZJInlHRiVGJiIiIkYrISIi">LCYmSSJ5RzYiNiMiIzYiIiJGKCEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> A 'for loop' can be written for the interior node points as</Text-field>
</Input>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do Eq[i]:=subs(m=i,Eq[m]);od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiIsJiomLCgmSSJ5R0YlNiMiIiNGJyomRi5GJyZGLEYmRichIiImRiw2IyIiIUYnRicpSSJoR0YlRi5GMUYnKiYpSSRQaGlHRiVGLkYnKUYwRi5GJ0Yx">LCYqJiwoJkkieUc2IjYjIiIjIiIiKiZGKUYqJkYmNiNGKkYqISIiJkYmNiMiIiFGKkYqKUkiaEdGJ0YpRi5GKiomKUkkUGhpR0YnRilGKilGLEYpRipGLg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiMsJiomLCgmSSJ5R0YlNiMiIiQiIiIqJkYnRi8mRixGJkYvISIiJkYsNiNGL0YvRi8pSSJoR0YlRidGMkYvKiYpSSRQaGlHRiVGJ0YvKUYxRidGL0Yy">LCYqJiwoJkkieUc2IjYjIiIkIiIiKiYiIiNGKiZGJjYjRixGKiEiIiZGJjYjRipGKkYqKUkiaEdGJ0YsRi9GKiomKUkkUGhpR0YnRixGKilGLUYsRipGLw==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiQsJiomLCgmSSJ5R0YlNiMiIiUiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjRjFGL0YvKUkiaEdGJUYxRjNGLyomKUkkUGhpR0YlRjFGLylGMkYxRi9GMw==">LCYqJiwoJkkieUc2IjYjIiIlIiIiKiYiIiNGKiZGJjYjIiIkRiohIiImRiY2I0YsRipGKilJImhHRidGLEYwRioqJilJJFBoaUdGJ0YsRiopRi1GLEYqRjA=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiUsJiomLCgmSSJ5R0YlNiMiIiYiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiIkRi9GLylJImhHRiVGMUYzRi8qJilJJFBoaUdGJUYxRi8pRjJGMUYvRjM=">LCYqJiwoJkkieUc2IjYjIiImIiIiKiYiIiNGKiZGJjYjIiIlRiohIiImRiY2IyIiJEYqRiopSSJoR0YnRixGMEYqKiYpSSRQaGlHRidGLEYqKUYtRixGKkYw</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiYsJiomLCgmSSJ5R0YlNiMiIiciIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiIlRi9GLylJImhHRiVGMUYzRi8qJilJJFBoaUdGJUYxRi8pRjJGMUYvRjM=">LCYqJiwoJkkieUc2IjYjIiInIiIiKiYiIiNGKiZGJjYjIiImRiohIiImRiY2IyIiJUYqRiopSSJoR0YnRixGMEYqKiYpSSRQaGlHRidGLEYqKUYtRixGKkYw</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIicsJiomLCgmSSJ5R0YlNiMiIigiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiImRi9GLylJImhHRiVGMUYzRi8qJilJJFBoaUdGJUYxRi8pRjJGMUYvRjM=">LCYqJiwoJkkieUc2IjYjIiIoIiIiKiYiIiNGKiZGJjYjIiInRiohIiImRiY2IyIiJkYqRiopSSJoR0YnRixGMEYqKiYpSSRQaGlHRidGLEYqKUYtRixGKkYw</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIigsJiomLCgmSSJ5R0YlNiMiIikiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiInRi9GLylJImhHRiVGMUYzRi8qJilJJFBoaUdGJUYxRi8pRjJGMUYvRjM=">LCYqJiwoJkkieUc2IjYjIiIpIiIiKiYiIiNGKiZGJjYjIiIoRiohIiImRiY2IyIiJ0YqRiopSSJoR0YnRixGMEYqKiYpSSRQaGlHRidGLEYqKUYtRixGKkYw</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiksJiomLCgmSSJ5R0YlNiMiIioiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiIoRi9GLylJImhHRiVGMUYzRi8qJilJJFBoaUdGJUYxRi8pRjJGMUYvRjM=">LCYqJiwoJkkieUc2IjYjIiIqIiIiKiYiIiNGKiZGJjYjIiIpRiohIiImRiY2IyIiKEYqRiopSSJoR0YnRixGMEYqKiYpSSRQaGlHRidGLEYqKUYtRixGKkYw</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiosJiomLCgmSSJ5R0YlNiMiIzUiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiIpRi9GLylJImhHRiVGMUYzRi8qJilJJFBoaUdGJUYxRi8pRjJGMUYvRjM=">LCYqJiwoJkkieUc2IjYjIiM1IiIiKiYiIiNGKiZGJjYjIiIqRiohIiImRiY2IyIiKUYqRiopSSJoR0YnRixGMEYqKiYpSSRQaGlHRidGLEYqKUYtRixGKkYw</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzUsJiomLCgmSSJ5R0YlNiMiIzYiIiIqJiIiI0YvJkYsRiZGLyEiIiZGLDYjIiIqRi9GLylJImhHRiVGMUYzRi8qJilJJFBoaUdGJUYxRi8pRjJGMUYvRjM=">LCYqJiwoJkkieUc2IjYjIiM2IiIiKiYiIiNGKiZGJjYjIiM1RiohIiImRiY2IyIiKkYqRiopSSJoR0YnRixGMEYqKiYpSSRQaGlHRidGLEYqKUYtRixGKkYw</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The node spacing is given by:</Text-field>
</Input>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">h:=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="L40" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">The value for \316\246 is sustained  in the governing equations.  The governing equations are stored in eqs:</Font></Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=seq(eval(subs(Phi=1,Eq[i])),i=0..N+1);</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="L41" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The variables are stored in vars:</Text-field>
</Input>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=seq(y[i],i=0..N+1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkldmFyc0c2IjYuJkkieUdGJDYjIiIhJkYnNiMiIiImRic2IyIiIyZGJzYjIiIkJkYnNiMiIiUmRic2IyIiJiZGJzYjIiInJkYnNiMiIigmRic2IyIiKSZGJzYjIiIqJkYnNiMiIzUmRic2IyIjNg==">Ni4mSSJ5RzYiNiMiIiEmRiQ2IyIiIiZGJDYjIiIjJkYkNiMiIiQmRiQ2IyIiJSZGJDYjIiImJkYkNiMiIicmRiQ2IyIiKCZGJDYjIiIpJkYkNiMiIiomRiQ2IyIjNSZGJDYjIiM2</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The 'fsolve' command sometimes gives negative values when guess values for the dependent variables are not provided.  To avoid this, an initial guess of 1 is provided:</Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">fsolve({eqs},{vars});</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">PC4vJkkieUc2IjYjIiM2JCIrKysrKzUhIiovJkYlNiMiIiMkIit3Qy4zcyEjNS8mRiU2IyIiISQiKzVsbEJyRjIvJkYlNiMiIiIkIissMHZXckYyLyZGJTYjIiIqJCIrZzUjeScqKUYyLyZGJTYjIiM1JCIrWz0uWiUqRjIvJkYlNiMiIiQkIit0SUQ5dEYyLyZGJTYjIiIlJCIrUnJva3VGMi8mRiU2IyIiJiQiK3c/PGh3RjIvJkYlNiMiIickIismM2toIXpGMi8mRiU2IyIiKCQiK0deIkc/KUYyLyZGJTYjIiIpJCIrImV1XWIpRjI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=seq(y[i]=1,i=0..N+1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkldmFyc0c2IjYuLyZJInlHRiQ2IyIiISIiIi8mRig2I0YrRisvJkYoNiMiIiNGKy8mRig2IyIiJEYrLyZGKDYjIiIlRisvJkYoNiMiIiZGKy8mRig2IyIiJ0YrLyZGKDYjIiIoRisvJkYoNiMiIilGKy8mRig2IyIiKkYrLyZGKDYjIiM1RisvJkYoNiMiIzZGKw==">Ni4vJkkieUc2IjYjIiIhIiIiLyZGJTYjRilGKS8mRiU2IyIiI0YpLyZGJTYjIiIkRikvJkYlNiMiIiVGKS8mRiU2IyIiJkYpLyZGJTYjIiInRikvJkYlNiMiIihGKS8mRiU2IyIiKUYpLyZGJTYjIiIqRikvJkYlNiMiIzVGKS8mRiU2IyIjNkYp</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=fsolve({eqs},{vars});</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkkc29sRzYiPC4vJkkieUdGJDYjIiIjJCIrd0MuM3MhIzUvJkYoNiMiIiEkIis1bGxCckYtLyZGKDYjIiIiJCIrLDB2V3JGLS8mRig2IyIiKiQiK2c1I3knKilGLS8mRig2IyIjNSQiK1s9LlolKkYtLyZGKDYjIiIkJCIrdElEOXRGLS8mRig2IyIiJSQiK1Jyb2t1Ri0vJkYoNiMiIiYkIit3Pzxod0YtLyZGKDYjIiInJCIrJjNraCF6Ri0vJkYoNiMiIigkIitHXiJHPylGLS8mRig2IyIiKSQiKyJldV1iKUYtLyZGKDYjIiM2JEY3RjE=">PC4vJkkieUc2IjYjIiIjJCIrd0MuM3MhIzUvJkYlNiMiIiEkIis1bGxCckYrLyZGJTYjIiIiJCIrLDB2V3JGKy8mRiU2IyIiKiQiK2c1I3knKilGKy8mRiU2IyIjNSQiK1s9LlolKkYrLyZGJTYjIiIkJCIrdElEOXRGKy8mRiU2IyIiJSQiK1Jyb2t1RisvJkYlNiMiIiYkIit3Pzxod0YrLyZGJTYjIiInJCIrJjNraCF6RisvJkYlNiMiIigkIitHXiJHPylGKy8mRiU2IyIiKSQiKyJldV1iKUYrLyZGJTYjIiM2JEY1Ri8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution obtained is assigned and plotted:</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">assign(sol):</Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([seq([i*h,y[i]],i=0..N+1)],thickness=4,axes=boxed,title=&quot;Figure Exp. 3.2.6.&quot;,labels=[x,y]);</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">NiktJSdDVVJWRVNHNiQ3LjckJCIiISEiIiQiKl5jTzcoISIqNyQkIjEiNDQ0NDQ0NCohIzwkIissMHZXciEjNTckJCIyIz09PT09PT09ISM8JCIrd0MuM3MhIzU3JCQiMUZGRkZGRkZGISM7JCIrdElEOXQhIzU3JCQiMmxqampqampqJCEjPCQiK1Jyb2t1ISM1NyQkIjJgYWFhYWFhYSUhIzwkIit3PzxodyEjNTckJCIxYWFhYWFhYWEhIzskIismM2toIXohIzU3JCQiMWtqampqampqISM7JCIxLCsrR14iRz8pISM7NyQkIjF0c3Nzc3NzcyEjOyQiKyJldV1iKSEjNTckJCIxIz09PT09PT0pISM7JCIqMUB5JyopISIqNyQkIjEiNDQ0NDQ0NCohIzskIitbPS5aJSohIzU3JCQiIzUhIiIkIiM1ISIiLSUmQ09MT1JHNiYlJFJHQkckIiM1ISIiJCIiISEiIiQiIiEhIiItJStBWEVTTEFCRUxTRzYnLUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2NVEieDYiLyUnZmFtaWx5R1EhNiIvJSVzaXplR1EjMTA2Ii8lJWJvbGRHUSZmYWxzZTYiLyUnaXRhbGljR1EldHJ1ZTYiLyUqdW5kZXJsaW5lR1EmZmFsc2U2Ii8lKnN1YnNjcmlwdEdRJmZhbHNlNiIvJSxzdXBlcnNjcmlwdEdRJmZhbHNlNiIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXTYiLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV02Ii8lJ29wYXF1ZUdRJmZhbHNlNiIvJStleGVjdXRhYmxlR1EmZmFsc2U2Ii8lKXJlYWRvbmx5R1EmZmFsc2U2Ii8lKWNvbXBvc2VkR1EmZmFsc2U2Ii8lKmNvbnZlcnRlZEdRJmZhbHNlNiIvJStpbXNlbGVjdGVkR1EmZmFsc2U2Ii8lLHBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJmZhbHNlNiIvJSxtYXRodmFyaWFudEdRJ2l0YWxpYzYiLUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2NVEieTYiLyUnZmFtaWx5R1EhNiIvJSVzaXplR1EjMTA2Ii8lJWJvbGRHUSZmYWxzZTYiLyUnaXRhbGljR1EldHJ1ZTYiLyUqdW5kZXJsaW5lR1EmZmFsc2U2Ii8lKnN1YnNjcmlwdEdRJmZhbHNlNiIvJSxzdXBlcnNjcmlwdEdRJmZhbHNlNiIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXTYiLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV02Ii8lJ29wYXF1ZUdRJmZhbHNlNiIvJStleGVjdXRhYmxlR1EmZmFsc2U2Ii8lKXJlYWRvbmx5R1EmZmFsc2U2Ii8lKWNvbXBvc2VkR1EmZmFsc2U2Ii8lKmNvbnZlcnRlZEdRJmZhbHNlNiIvJStpbXNlbGVjdGVkR1EmZmFsc2U2Ii8lLHBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJmZhbHNlNiIvJSxtYXRodmFyaWFudEdRJ2l0YWxpYzYiLSUlRk9OVEc2JSUhRyUhRyIjNSUrSE9SSVpPTlRBTEclK0hPUklaT05UQUxHLSUmVElUTEVHNiQtJSlfVFlQRVNFVEc2I1EzRmlndXJlfkV4cC5+My4yLjYuNiItJS1UUkFOU1BBUkVOQ1lHNiMkIiIhISIiLSUqVEhJQ0tORVNTRzYjIiIkLSUqQVhFU1NUWUxFRzYjJSRCT1hHLSUoU0NBTElOR0c2IyUuVU5DT05TVFJBSU5FREctJSVST09URzYnLSUpQk9VTkRTX1hHNiMkIiRdJiEiIi0lKUJPVU5EU19ZRzYjJCIkcSMhIiItJS1CT1VORFNfV0lEVEhHNiMkIiU/TCEiIi0lLkJPVU5EU19IRUlHSFRHNiMkIiUhSCMhIiItJSlDSElMRFJFTkc2Ig==</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The accuracy of the solution obtained can be checked by following the concentration at the center y[0] and increasing the number of node points:</Text-field>
</Input>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">y[0];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIrNWxsQnIhIzU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>