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<Input>
<Text-field style="Text" layout="Normal">Example 5.2.4 Exothermal Reaction in a Sphere</Text-field>
</Input>
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<Group labelreference="L45" 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(linalg):with(plots):</Text-field>
</Input>
</Group>
<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)+beta*exp(-E/R/(u(x,t)+273.16));;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZ2VHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkidEdGJEYuLCgtRic2JEYqLUkiJEdGKDYkRi0iIiMiIiIqKEY1RjZGLSEiIi1GJzYkRipGLUY2RjYqJkklYmV0YUdGJEY2LUkkZXhwRzYkRihJKF9zeXNsaWJHRiQ2IywkKihJIkVHRiRGNkkiUkdGJEY4LCZGKkY2JCImO3QjISIjRjZGOEY4RjZGNg==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLCwoLUYkNiQtRiQ2JEYnRitGKyIiIiomRishIiJGMEYyIiIjKiZJJWJldGFHRilGMi1JJGV4cEc2JEYlSShfc3lzbGliR0YpNiMsJCooSSJFR0YpRjJJIlJHRilGNCwmRidGMiQiJjt0IyEiI0YyRjRGNEYyRjI=</Equation></Text-field>
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<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=diff(u(x,t),x);;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkidEdGJEYs">LUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHNiI2JEkieEdGKEkidEdGKEYq</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)-158;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLCYtSSJ1R0YkNiRJInhHRiRJInRHRiQiIiIiJGUiISIi">LCYtSSJ1RzYiNiRJInhHRiVJInRHRiUiIiIhJGUiRik=</Equation></Text-field>
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<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IC:=u(x,0)=25;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSUNHNiIvLUkidUdGJDYkSSJ4R0YkIiIhIiNE">Ly1JInVHNiI2JEkieEdGJSIiISIjRA==</Equation></Text-field>
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<Group labelreference="L8" 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>
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</Group>
<Group labelreference="L9" 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>
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<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">beta:=6.699e17;E:=30800;R:=1.987;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklYmV0YUc2IiQiJSpwJyIjOQ==">JCIlKnAnIiM5</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiRUc2IiImKzMk">IiYrMyQ=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiUkc2IiQiJSgpPiEiJA==">JCIlKCk+ISIk</Equation></Text-field>
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<Group labelreference="L11" drawlabel="true">
<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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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGZHNiIsJCooIyIiIiIiI0YoLCgtJkkidUdGJDYjRik2I0kidEdGJCEiIiomIiIkRigtJkYtNiMiIiFGL0YoRjEqJiIiJUYoLSZGLTYjRihGL0YoRihGKEkiaEdGJEYxRig=">LCQqJiwoLSZJInVHNiI2IyIiIzYjSSJ0R0YoISIiLSZGJzYjIiIhRishIiQtJkYnNiMiIiJGKyIiJUY2SSJoR0YoRi0jRjZGKg==</Equation></Text-field>
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<Group labelreference="L12" drawlabel="true">
<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>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGJHNiIsJCooIyIiIiIiI0YoLCgtJkkidUdGJDYjIiIqNiNJInRHRiRGKComIiIkRigtJkYtNiMiIzZGMEYoRigqJiIiJUYoLSZGLTYjIiM1RjBGKCEiIkYoSSJoR0YkRj5GKA==">LCQqJiwoLSZJInVHNiI2IyIiKjYjSSJ0R0YoIiIiLSZGJzYjIiM2RisiIiQtJkYnNiMiIzVGKyEiJUYtSSJoR0YoISIiI0YtIiIj</Equation></Text-field>
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<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydx:=1/2/h*(u[m+1](t)-u[m-1](t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklZHlkeEc2IiwkKigjIiIiIiIjRihJImhHRiQhIiIsJi0mSSJ1R0YkNiMsJkkibUdGJEYoRihGKDYjSSJ0R0YkRigtJkYvNiMsJkYyRihGKEYrRjNGK0YoRig=">LCQqJkkiaEc2IiEiIiwmLSZJInVHRiU2IywmSSJtR0YlIiIiRi5GLjYjSSJ0R0YlRi4tJkYqNiMsJkYtRi5GJkYuRi9GJkYuI0YuIiIj</Equation></Text-field>
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<Group labelreference="L14" drawlabel="true">
<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>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknZDJ5ZHgyRzYiKiYpSSJoR0YkIiIjISIiLCgtJkkidUdGJDYjLCZJIm1HRiQiIiJGMUYpNiNJInRHRiRGMSomRihGMS0mRi02I0YwRjJGMUYpLSZGLTYjLCZGMEYxRjFGMUYyRjFGMQ==">KiZJImhHNiIhIiMsKC0mSSJ1R0YkNiMsJkkibUdGJCIiIiEiIkYtNiNJInRHRiRGLS0mRik2I0YsRi9GJS0mRik2IywmRixGLUYtRi1GL0YtRi0=</Equation></Text-field>
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<Group labelreference="L15" 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),x=0,bc1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLCQqKCMiIiIiIiNGKCwoLSZJInVHRiQ2I0YpNiNJInRHRiQhIiIqJiIiJEYoLSZGLTYjIiIhRi9GKEYxKiYiIiVGKC0mRi02I0YoRi9GKEYoRihJImhHRiRGMUYo">LCQqJiwoLSZJInVHNiI2IyIiIzYjSSJ0R0YoISIiLSZGJzYjIiIhRishIiQtJkYnNiMiIiJGKyIiJUY2SSJoR0YoRi0jRjZGKg==</Equation></Text-field>
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<Group labelreference="L16" 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),x=1,bc2);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLCYtJkkidUdGJDYjIiM2NiNJInRHRiQiIiIiJGUiISIi">LCYtJkkidUc2IjYjIiM2NiNJInRHRiYiIiIhJGUiRis=</Equation></Text-field>
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<Group labelreference="L17" 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="PiZJI2VxRzYiNiMiIiEsJCooIyIiIiIiI0YrLCgtJkkidUdGJTYjRiw2I0kidEdGJSEiIiomIiIkRistJkYwRiZGMkYrRjQqJiIiJUYrLSZGMDYjRitGMkYrRitGK0kiaEdGJUY0Ris=">LCQqJiwoLSZJInVHNiI2IyIiIzYjSSJ0R0YoISIiLSZGJzYjIiIhRishIiQtJkYnNiMiIiJGKyIiJUY2SSJoR0YoRi0jRjZGKg==</Equation></Text-field>
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<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[N+1]:=bc2; </Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzYsJi0mSSJ1R0YlRiY2I0kidEdGJSIiIiIkZSIhIiI=">LCYtJkkidUc2IjYjIiM2NiNJInRHRiYiIiIhJGUiRis=</Equation></Text-field>
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<Group labelreference="L19" 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=i*h,rhs(ge));od:</Text-field>
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<Group labelreference="L20" 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="Pi0mSSJ1RzYiNiMiIiE2I0kidEdGJiwmKiYjIiIiIiIkRi4tJkYlNiMiIiNGKUYuISIiKiYjIiIlRi9GLi0mRiU2I0YuRilGLkYu">LCYtJkkidUc2IjYjIiIjNiNJInRHRiYjISIiIiIkLSZGJTYjIiIiRikjIiIlRi0=</Equation></Text-field>
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<Group labelreference="L21" 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="Pi0mSSJ1RzYiNiMiIzY2I0kidEdGJiIkZSI=">IiRlIg==</Equation></Text-field>
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<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>
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</Group>
<Group labelreference="L23" 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>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=seq((eq[j]),j=1..N):</Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=seq(u[i](t),i=1..N);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiWUc2IjYsLSZJInVHRiQ2IyIiIjYjSSJ0R0YkLSZGKDYjIiIjRistJkYoNiMiIiRGKy0mRig2IyIiJUYrLSZGKDYjIiImRistJkYoNiMiIidGKy0mRig2IyIiKEYrLSZGKDYjIiIpRistJkYoNiMiIipGKy0mRig2IyIjNUYr">NiwtJkkidUc2IjYjIiIiNiNJInRHRiYtJkYlNiMiIiNGKS0mRiU2IyIiJEYpLSZGJTYjIiIlRiktJkYlNiMiIiZGKS0mRiU2IyIiJ0YpLSZGJTYjIiIoRiktJkYlNiMiIilGKS0mRiU2IyIiKkYpLSZGJTYjIiM1Rik=</Equation></Text-field>
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<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ICs:=seq(u[i](0)=rhs(IC),i=1..N);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkSUNzRzYiNiwvLSZJInVHRiQ2IyIiIjYjIiIhIiNELy0mRik2IyIiI0YsRi4vLSZGKTYjIiIkRixGLi8tJkYpNiMiIiVGLEYuLy0mRik2IyIiJkYsRi4vLSZGKTYjIiInRixGLi8tJkYpNiMiIihGLEYuLy0mRik2IyIiKUYsRi4vLSZGKTYjIiIqRixGLi8tJkYpNiMiIzVGLEYu">NiwvLSZJInVHNiI2IyIiIjYjIiIhIiNELy0mRiY2IyIiI0YqRiwvLSZGJjYjIiIkRipGLC8tJkYmNiMiIiVGKkYsLy0mRiY2IyIiJkYqRiwvLSZGJjYjIiInRipGLC8tJkYmNiMiIihGKkYsLy0mRiY2IyIiKUYqRiwvLSZGJjYjIiIqRipGLC8tJkYmNiMiIzVGKkYs</Equation></Text-field>
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<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Maple's stiff solver (Rosenbrock algorithm) is used by setting the option stiff = true:</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqs,ICs},{Y},type=numeric,stiff=true,output=listprocedure);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 4148 characters]">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" 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="L29" 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="PiZJIlVHNiI2IyIiISwmKiYjIiIiIiIkRismRiQ2IyIiI0YrISIiKiYjIiIlRixGKyZGJDYjRitGK0Yr">LCYmSSJVRzYiNiMiIiMjISIiIiIkJkYkNiMiIiIjIiIlRio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" 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="PiZJIlVHNiI2IyIjNiIkZSI=">IiRlIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 do p[i]:=plot(U[i](t),t=0..0.4,thickness=3);od:</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({seq(p[i],i=0..N+1)},axes=boxed,title=&quot;Figure Exp. 5.2.7.&quot;,labels=[t,&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, 24612 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tf:=0.3784;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdGZHNiIkIiUleSQhIiU=">JCIlJXkkISIl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" 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="L35" 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="PkkjVDFHNiI3QSQiIiFGJyQiK0xMTGg3ISM2JCIrbm1tQURGKiQiKysrKyV5JEYqJCIrTExMWF1GKiQiK25tbTFqRiokIisrKytvdkYqJCIrTExMSCkpRiokIitubTE0NSEjNSQiKysrP042RjkkRilGOSQiK25tWShRIkY5JCIrKytnODpGOSQiK0xMdFI7RjkkIitubSdldyJGOSQiKysrKyMqPUY5JCIrTEw4PT9GOSQiK25tRVdARjkkIisrK1NxQUY5JCIrTExgJ1IjRjkkRixGOSQiKysrISlbRUY5JCIrTEwkXHgjRjkkIitubTEsSEY5JCIrKys/RklGOSQiK0xMTGBKRjkkIitubVl6S0Y5JCIrKytnME1GOSQiK0xMdEpORjkkIitubSd5bCRGOSRGLkY5">N0EkIiIhRiQkIitMTExoNyEjNiQiK25tbUFERickIisrKysleSRGJyQiK0xMTFhdRickIitubW0xakYnJCIrKysrb3ZGJyQiK0xMTEgpKUYnJCIrbm0xNDUhIzUkIisrKz9ONkY2JEYmRjYkIitubVkoUSJGNiQiKysrZzg6RjYkIitMTHRSO0Y2JCIrbm0nZXciRjYkIisrKysjKj1GNiQiK0xMOD0/RjYkIitubUVXQEY2JCIrKytTcUFGNiQiK0xMYCdSI0Y2JEYpRjYkIisrKyEpW0VGNiQiK0xMJFx4I0Y2JCIrbm0xLEhGNiQiKysrP0ZJRjYkIitMTExgSkY2JCIrbm1ZektGNiQiKysrZzBNRjYkIitMTHRKTkY2JCIrbm0neWwkRjYkRitGNg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" 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="L37" 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)*h,rhs(IC)));od:</Text-field>
</Input>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N+2 do for j from 2 to M+1 do PP[i,j]:=evalf(subs(t=T1[j],U[i-1](t)));od;od:</Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plotdata := [seq([ seq([(i-1)*h,T1[j],PP[i,j]], i=1..N+2)], j=1..M+1)]:</Text-field>
</Input>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">surfdata(plotdata,axes=boxed,title=&quot;Figure Exp. 5.2.8.&quot;,labels=[x,t,u],orientation=[-45,60]);</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, 17772 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The center of the sphere explodes after t = 0.3784 and the numerical calculations stop:</Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(U[0](t),t=0..1,thickness=3,title=&quot;Figure 5.2.9.&quot;,axes=boxed,labels=[t,&quot;u[0]&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="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">px[0]:=plot([seq([i*h,subs(x=i*h,rhs(IC))],i=0..N+1)],thickness=3):</Text-field>
</Input>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for j from 2 to M+1 do px[j]:=plot([seq([i*h,U[i](T1[j])],i=0..N+1)],thickness=3):od:;</Text-field>
</Input>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({seq(px[j*2],j=0..(M+1)/2)},title=&quot;Figure 5.2.10.&quot;,axes=boxed,labels=[x,u]);</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, 10760 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>