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<Input>
<Text-field style="Text" layout="Normal">Example 5.2.1 Diffusion with Second Order Reaction</Text-field>
</Input>
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<Group labelreference="L43" 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>
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<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)-Phi^2*u(x,t)^2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZ2VHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkidEdGJEYuLCYtRic2JEYqLUkiJEdGKDYkRi0iIiMiIiIqJilJJFBoaUdGJEY1RjYpRipGNUY2ISIi">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLCwmLUYkNiQtRiQ2JEYnRitGKyIiIiomKUkkUGhpR0YpIiIjRjIpRidGNkYyISIi</Equation></Text-field>
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<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=u(x,t)-1;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLCYtSSJ1R0YkNiRJInhHRiRJInRHRiQiIiJGKyEiIg==">LCYtSSJ1RzYiNiRJInhHRiVJInRHRiUiIiJGKSEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=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="PkkkYmMyRzYiLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkidEdGJEYs">LUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHNiI2JEkieEdGKEkidEdGKEYq</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)=0;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSUNHNiIvLUkidUdGJDYkSSJ4R0YkIiIhRio=">Ly1JInVHNiI2JEkieEdGJSIiIUYo</Equation></Text-field>
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</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=10;</Text-field>
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<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>
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<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">Phi:=1;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkUGhpRzYiIiIi">IiIi</Equation></Text-field>
</Output>
</Group>
<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>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGZHNiIsJCooIyIiIiIiI0YoLCgtJkkidUdGJDYjRik2I0kidEdGJCEiIiomIiIkRigtJkYtNiMiIiFGL0YoRjEqJiIiJUYoLSZGLTYjRihGL0YoRihGKEkiaEdGJEYxRig=">LCQqKCMiIiIiIiNGJSwoLSZJInVHNiI2I0YmNiNJInRHRishIiIqJiIiJEYlLSZGKjYjIiIhRi1GJUYvKiYiIiVGJS0mRio2I0YlRi1GJUYlRiVJImhHRitGL0Yl</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>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGJHNiIsJCooIyIiIiIiI0YoLCgtJkkidUdGJDYjIiIqNiNJInRHRiRGKComIiIkRigtJkYtNiMiIzZGMEYoRigqJiIiJUYoLSZGLTYjIiM1RjBGKCEiIkYoSSJoR0YkRj5GKA==">LCQqKCMiIiIiIiNGJSwoLSZJInVHNiI2IyIiKjYjSSJ0R0YrRiUqJiIiJEYlLSZGKjYjIiM2Ri5GJUYlKiYiIiVGJS0mRio2IyIjNUYuRiUhIiJGJUkiaEdGK0Y8RiU=</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=">LCQqKCMiIiIiIiNGJUkiaEc2IiEiIiwmLSZJInVHRig2IywmSSJtR0YoRiVGJUYlNiNJInRHRihGJS0mRi02IywmRjBGJUYlRilGMUYpRiVGJQ==</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>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknZDJ5ZHgyRzYiKiYpSSJoR0YkIiIjISIiLCgtJkkidUdGJDYjLCZJIm1HRiQiIiJGMUYpNiNJInRHRiRGMSomRihGMS0mRi02I0YwRjJGMUYpLSZGLTYjLCZGMEYxRjFGMUYyRjFGMQ==">KiYpSSJoRzYiIiIjISIiLCgtJkkidUdGJTYjLCZJIm1HRiUiIiJGL0YnNiNJInRHRiVGLyomRiZGLy0mRis2I0YuRjBGL0YnLSZGKzYjLCZGLkYvRi9GL0YwRi9GLw==</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>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLCYtJkkidUdGJDYjIiIhNiNJInRHRiQiIiJGLSEiIg==">LCYtJkkidUc2IjYjIiIhNiNJInRHRiYiIiJGKyEiIg==</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>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLCQqKCMiIiIiIiNGKCwoLSZJInVHRiQ2IyIiKjYjSSJ0R0YkRigqJiIiJEYoLSZGLTYjIiM2RjBGKEYoKiYiIiVGKC0mRi02IyIjNUYwRighIiJGKEkiaEdGJEY+Rig=">LCQqKCMiIiIiIiNGJSwoLSZJInVHNiI2IyIiKjYjSSJ0R0YrRiUqJiIiJEYlLSZGKjYjIiM2Ri5GJUYlKiYiIiVGJS0mRio2IyIjNUYuRiUhIiJGJUkiaEdGK0Y8RiU=</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="PiZJI2VxRzYiNiMiIiEsJi0mSSJ1R0YlRiY2I0kidEdGJSIiIkYuISIi">LCYtJkkidUc2IjYjIiIhNiNJInRHRiYiIiJGKyEiIg==</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="PiZJI2VxRzYiNiMiIzYsJCooIyIiIiIiI0YrLCgtJkkidUdGJTYjIiIqNiNJInRHRiVGKyomIiIkRistJkYwRiZGM0YrRisqJiIiJUYrLSZGMDYjIiM1RjNGKyEiIkYrSSJoR0YlRj9GKw==">LCQqKCMiIiIiIiNGJSwoLSZJInVHNiI2IyIiKjYjSSJ0R0YrRiUqJiIiJEYlLSZGKjYjIiM2Ri5GJUYlKiYiIiVGJS0mRio2IyIjNUYuRiUhIiJGJUkiaEdGK0Y8RiU=</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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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJImhHRiUiIiMhIiIsKC0mRi82IyIiIUYwRicqJkY2RidGLUYnRjctJkYvNiNGNkYwRidGJ0YnKiQpRi1GNkYnRjc=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIiNiNJInRHRipGLiwmKiYpSSJoR0YqIiIjISIiLCgtJkYpNiMiIiFGLUYsKiZGM0YsRidGLEY0LSZGKTYjRjNGLUYsRixGLCokKUYnRjNGLEY0</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJImhHRiVGJyEiIiwoLSZGLzYjIiIiRjBGOyomRidGO0YtRjtGNi0mRi82IyIiJEYwRjtGO0Y7KiQpRi1GJ0Y7RjY=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIjNiNJInRHRipGLiwmKiYpSSJoR0YqRiwhIiIsKC0mRik2IyIiIkYtRjgqJkYsRjhGJ0Y4RjMtJkYpNiMiIiRGLUY4RjhGOCokKUYnRixGOEYz</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJImhHRiUiIiMhIiIsKC0mRi82I0Y2RjAiIiIqJkY2RjxGLUY8RjctJkYvNiMiIiVGMEY8RjxGPCokKUYtRjZGPEY3">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIkNiNJInRHRipGLiwmKiYpSSJoR0YqIiIjISIiLCgtJkYpNiNGM0YtIiIiKiZGM0Y5RidGOUY0LSZGKTYjIiIlRi1GOUY5RjkqJClGJ0YzRjlGNA==</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCYqJilJImhHRiUiIiMhIiIsKC0mRi82IyIiKkYwIiIiKiZGNkY9Ri1GPUY3LSZGLzYjIiM2RjBGPUY9Rj0qJClGLUY2Rj1GNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiM1NiNJInRHRipGLiwmKiYpSSJoR0YqIiIjISIiLCgtJkYpNiMiIipGLSIiIiomRjNGOkYnRjpGNC0mRik2IyIjNkYtRjpGOkY6KiQpRidGM0Y6RjQ=</Equation></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="Pi0mSSJ1RzYiNiMiIiE2I0kidEdGJiIiIg==">IiIi</Equation></Text-field>
</Output>
</Group>
<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="Pi0mSSJ1RzYiNiMiIzY2I0kidEdGJiwmKiYjIiIiIiIkRi4tJkYlNiMiIipGKUYuISIiKiYjIiIlRi9GLi0mRiU2IyIjNUYpRi5GLg==">LCYqJiMiIiIiIiRGJS0mSSJ1RzYiNiMiIio2I0kidEdGKkYlISIiKiYjIiIlRiZGJS0mRik2IyIjNUYtRiVGJQ==</Equation></Text-field>
</Output>
</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="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>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCoiJEAiRicqJiIkVSNGJ0YtRichIiIqJkYzRictJkYvNiMiIiNGMEYnRicqJClGLUY7RidGNg==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIiNiNJInRHRipGLiwqIiRAIkYsKiYiJFUjRixGJ0YsISIiKiZGMEYsLSZGKTYjIiIjRi1GLEYsKiQpRidGOEYsRjM=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCoqJiIkQCIiIiItJkYvNiNGNUYwRjVGNSomIiRVI0Y1Ri1GNSEiIiomRjRGNS0mRi82IyIiJEYwRjVGNSokKUYtRidGNUY7">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIjNiNJInRHRipGLiwqKiYiJEAiIiIiLSZGKTYjRjJGLUYyRjIqJiIkVSNGMkYnRjIhIiIqJkYxRjItJkYpNiMiIiRGLUYyRjIqJClGJ0YsRjJGOA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCoqJiIkQCIiIiItJkYvNiMiIiNGMEY1RjUqJiIkVSNGNUYtRjUhIiIqJkY0RjUtJkYvNiMiIiVGMEY1RjUqJClGLUY5RjVGPA==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIkNiNJInRHRipGLiwqKiYiJEAiIiIiLSZGKTYjIiIjRi1GMkYyKiYiJFUjRjJGJ0YyISIiKiZGMUYyLSZGKTYjIiIlRi1GMkYyKiQpRidGNkYyRjk=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCoqJiIkQCIiIiItJkYvNiMiIiRGMEY1RjUqJiIkVSNGNUYtRjUhIiIqJkY0RjUtJkYvNiMiIiZGMEY1RjUqJClGLSIiI0Y1Rjw=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIlNiNJInRHRipGLiwqKiYiJEAiIiIiLSZGKTYjIiIkRi1GMkYyKiYiJFUjRjJGJ0YyISIiKiZGMUYyLSZGKTYjIiImRi1GMkYyKiQpRiciIiNGMkY5</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiYvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCoqJiIkQCIiIiItJkYvNiMiIiVGMEY1RjUqJiIkVSNGNUYtRjUhIiIqJkY0RjUtJkYvNiMiIidGMEY1RjUqJClGLSIiI0Y1Rjw=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiImNiNJInRHRipGLiwqKiYiJEAiIiIiLSZGKTYjIiIlRi1GMkYyKiYiJFUjRjJGJ0YyISIiKiZGMUYyLSZGKTYjIiInRi1GMkYyKiQpRiciIiNGMkY5</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIicvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCoqJiIkQCIiIiItJkYvNiMiIiZGMEY1RjUqJiIkVSNGNUYtRjUhIiIqJkY0RjUtJkYvNiMiIihGMEY1RjUqJClGLSIiI0Y1Rjw=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiInNiNJInRHRipGLiwqKiYiJEAiIiIiLSZGKTYjIiImRi1GMkYyKiYiJFUjRjJGJ0YyISIiKiZGMUYyLSZGKTYjIiIoRi1GMkYyKiQpRiciIiNGMkY5</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIigvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCoqJiIkQCIiIiItJkYvNiMiIidGMEY1RjUqJiIkVSNGNUYtRjUhIiIqJkY0RjUtJkYvNiMiIilGMEY1RjUqJClGLSIiI0Y1Rjw=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIoNiNJInRHRipGLiwqKiYiJEAiIiIiLSZGKTYjIiInRi1GMkYyKiYiJFUjRjJGJ0YyISIiKiZGMUYyLSZGKTYjIiIpRi1GMkYyKiQpRiciIiNGMkY5</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIikvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCoqJiIkQCIiIiItJkYvNiMiIihGMEY1RjUqJiIkVSNGNUYtRjUhIiIqJkY0RjUtJkYvNiMiIipGMEY1RjUqJClGLSIiI0Y1Rjw=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIpNiNJInRHRipGLiwqKiYiJEAiIiIiLSZGKTYjIiIoRi1GMkYyKiYiJFUjRjJGJ0YyISIiKiZGMUYyLSZGKTYjIiIqRi1GMkYyKiQpRiciIiNGMkY5</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiovLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCoqJiIkQCIiIiItJkYvNiMiIilGMEY1RjUqJiIkVSNGNUYtRjUhIiIqJkY0RjUtJkYvNiMiIzVGMEY1RjUqJClGLSIiI0Y1Rjw=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIqNiNJInRHRipGLiwqKiYiJEAiIiIiLSZGKTYjIiIpRi1GMkYyKiYiJFUjRjJGJ0YyISIiKiZGMUYyLSZGKTYjIiM1Ri1GMkYyKiQpRiciIiNGMkY5</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCgqJiMiJFUjIiIkIiIiLSZGLzYjIiIqRjBGN0Y3KiZGNEY3Ri1GNyEiIiokKUYtIiIjRjdGPQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiM1NiNJInRHRipGLiwoKiYjIiRVIyIiJCIiIi0mRik2IyIiKkYtRjRGNComRjFGNEYnRjQhIiIqJClGJyIiI0Y0Rjo=</Equation></Text-field>
</Output>
</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>
<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="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>
</Output>
</Group>
<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="PkkkSUNzRzYiNiwvLSZJInVHRiQ2IyIiIjYjIiIhRi0vLSZGKTYjIiIjRixGLS8tJkYpNiMiIiRGLEYtLy0mRik2IyIiJUYsRi0vLSZGKTYjIiImRixGLS8tJkYpNiMiIidGLEYtLy0mRik2IyIiKEYsRi0vLSZGKTYjIiIpRixGLS8tJkYpNiMiIipGLEYtLy0mRik2IyIjNUYsRi0=">NiwvLSZJInVHNiI2IyIiIjYjIiIhRisvLSZGJjYjIiIjRipGKy8tJkYmNiMiIiRGKkYrLy0mRiY2IyIiJUYqRisvLSZGJjYjIiImRipGKy8tJkYmNiMiIidGKkYrLy0mRiY2IyIiKEYqRisvLSZGJjYjIiIpRipGKy8tJkYmNiMiIipGKkYrLy0mRiY2IyIjNUYqRis=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqs,ICs},{Y},type=numeric,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]">[encoded data, 4116 characters]</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="PiZJIlVHNiI2IyIiISIiIg==">IiIi</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="PiZJIlVHNiI2IyIjNiwmKiYjIiIiIiIkRismRiQ2IyIiKkYrISIiKiYjIiIlRixGKyZGJDYjIiM1RitGKw==">LCYqJiMiIiIiIiRGJSZJIlVHNiI2IyIiKkYlISIiKiYjIiIlRiZGJSZGKDYjIiM1RiVGJQ==</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="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pp:=plot([seq(U[i](t),i=0..N+1)],t=0..0.4);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 15608 characters]">[encoded data, 15580 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display(pp,title=&quot;Figure 5.2.1.&quot;,axes=boxed,thickness=4,labels=[t,&quot;u&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, 23376 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tf:=0.4;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdGZHNiIkIiIlISIi">JCIiJSEiIg==</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="PkkjVDFHNiI3QSQiIiFGJyQiK0xMTEw4ISM2JCIrbm1tbUVGKiQiKysrKytTRiokIitMTExMYEYqJCIrbm1tbW1GKiQiKysrKyshKUYqJCIrTExMTCQqRiokIitubW1tNSEjNSQiKysrKys3RjkkRilGOSQiK25tbW05RjkkIisrKysrO0Y5JCIrTExMTDxGOSQiK25tbW09RjkkIisrKysrP0Y5JCIrTExMTEBGOSQiK25tbW1BRjkkIisrKysrQ0Y5JCIrTExMTERGOSRGLEY5JCIrKysrK0dGOSQiK0xMTExIRjkkIitubW1tSUY5JCIrKysrK0tGOSQiK0xMTExMRjkkIitubW1tTUY5JCIrKysrK09GOSQiK0xMTExQRjkkIitubW1tUUY5JEYuRjk=">N0EkIiIhRiQkIitMTExMOCEjNiQiK25tbW1FRickIisrKysrU0YnJCIrTExMTGBGJyQiK25tbW1tRickIisrKysrISlGJyQiK0xMTEwkKkYnJCIrbm1tbTUhIzUkIisrKysrN0Y2JEYmRjYkIitubW1tOUY2JCIrKysrKztGNiQiK0xMTEw8RjYkIitubW1tPUY2JCIrKysrKz9GNiQiK0xMTExARjYkIitubW1tQUY2JCIrKysrK0NGNiQiK0xMTExERjYkRilGNiQiKysrKytHRjYkIitMTExMSEY2JCIrbm1tbUlGNiQiKysrKytLRjYkIitMTExMTEY2JCIrbm1tbU1GNiQiKysrKytPRjYkIitMTExMUEY2JCIrbm1tbVFGNiRGK0Y2</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. 5.2.2.&quot;,labels=[x,t,u],orientation=[-45,60]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="three-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0">[encoded data, 17596 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>