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<Text-field style="Text" layout="Normal">Example 5.7 Semianalytical Method for PDEs wtih Known Initial Profiles</Text-field>
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<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart;</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(linalg):with(plots):</Text-field>
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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)=Ds*diff(u(x,t),x$2);</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZ2VHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkidEdGJEYuKiZJI0RzR0YkIiIiLUYnNiRGKi1JIiRHRig2JEYtIiIjRjE=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLComSSNEc0dGKSIiIi1GJDYkLUYkNiRGJ0YrRitGLw==</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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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkidEdGJEYs">LUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHNiI2JEkieEdGKEkidEdGKEYq</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=u(x,t);</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLUkidUdGJDYkSSJ4R0YkSSJ0R0Yk">LUkidUc2IjYkSSJ4R0YkSSJ0R0Yk</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IC:=u(x,0)=cos(Pi*x/2/L);</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSUNHNiIvLUkidUdGJDYkSSJ4R0YkIiIhLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJCoqIyIiIiIiI0Y0SSNQaUdGLkY0RilGNEkiTEdGJCEiIkY0">Ly1JInVHNiI2JEkieEdGJSIiIS1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCQqKEkjUGlHRiwiIiJGJ0YySSJMR0YlISIiI0YyIiIj</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">L:=0.02;</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTEc2IiQiIiMhIiM=">JCIiIyEiIw==</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ds:=2e-5;</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjRHNHNiIkIiIjISIm">JCIiIyEiJg==</Equation></Text-field>
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<Group labelreference="L10" drawlabel="true">
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=10;</Text-field>
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<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 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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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGZHNiIsJCooIyIiIiIiI0YoLCgtJkkidUdGJDYjRik2I0kidEdGJCEiIiomIiIkRigtJkYtNiMiIiFGL0YoRjEqJiIiJUYoLSZGLTYjRihGL0YoRihGKEkiaEdGJEYxRig=">LCQqJiwoLSZJInVHNiI2IyIiIzYjSSJ0R0YoISIiLSZGJzYjIiIhRishIiQtJkYnNiMiIiJGKyIiJUY2SSJoR0YoRi0jRjZGKg==</Equation></Text-field>
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<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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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkeGJHNiIsJCooIyIiIiIiI0YoLCgtJkkidUdGJDYjIiIqNiNJInRHRiRGKComIiIkRigtJkYtNiMiIzZGMEYoRigqJiIiJUYoLSZGLTYjIiM1RjBGKCEiIkYoSSJoR0YkRj5GKA==">LCQqJiwoLSZJInVHNiI2IyIiKjYjSSJ0R0YoIiIiLSZGJzYjIiM2RisiIiQtJkYnNiMiIzVGKyEiJUYtSSJoR0YoISIiI0YtIiIj</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydx:=1/2/h*(u[m+1](t)-u[m-1](t));</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklZHlkeEc2IiwkKigjIiIiIiIjRihJImhHRiQhIiIsJi0mSSJ1R0YkNiMsJkkibUdGJEYoRihGKDYjSSJ0R0YkRigtJkYvNiMsJkYyRihGKEYrRjNGK0YoRig=">LCQqJkkiaEc2IiEiIiwmLSZJInVHRiU2IywmSSJtR0YlIiIiRi5GLjYjSSJ0R0YlRi4tJkYqNiMsJkYtRi5GJkYuRi9GJkYuI0YuIiIj</Equation></Text-field>
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<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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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknZDJ5ZHgyRzYiKiYpSSJoR0YkIiIjISIiLCgtJkkidUdGJDYjLCZJIm1HRiQiIiJGMUYpNiNJInRHRiRGMSomRihGMS0mRi02I0YwRjJGMUYpLSZGLTYjLCZGMEYxRjFGMUYyRjFGMQ==">KiZJImhHNiIhIiMsKC0mSSJ1R0YkNiMsJkkibUdGJCIiIiEiIkYtNiNJInRHRiRGLS0mRik2I0YsRi9GJS0mRik2IywmRixGLUYtRi1GL0YtRi0=</Equation></Text-field>
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<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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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLCQqKCMiIiIiIiNGKCwoLSZJInVHRiQ2I0YpNiNJInRHRiQhIiIqJiIiJEYoLSZGLTYjIiIhRi9GKEYxKiYiIiVGKC0mRi02I0YoRi9GKEYoRihJImhHRiRGMUYo">LCQqJiwoLSZJInVHNiI2IyIiIzYjSSJ0R0YoISIiLSZGJzYjIiIhRishIiQtJkYnNiMiIiJGKyIiJUY2SSJoR0YoRi0jRjZGKg==</Equation></Text-field>
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<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="PkkkYmMyRzYiLSZJInVHRiQ2IyIjNjYjSSJ0R0Yk">LSZJInVHNiI2IyIjNjYjSSJ0R0Yl</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[0]:=bc1; </Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[N+1]:=bc2; </Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzYtJkkidUdGJUYmNiNJInRHRiU=">LSZJInVHNiI2IyIjNjYjSSJ0R0Yl</Equation></Text-field>
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<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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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u[0](t):=(solve(eq[0],u[0](t)));</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="Pi0mSSJ1RzYiNiMiIzY2I0kidEdGJiIiIQ==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" 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="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCQqKCQiIiMhIiZGJylJImhHRiVGNSEiIiwmKiYjRjUiIiRGJy0mRi82I0Y1RjBGJ0YnKiZGPEYnRi1GJ0Y5RidGJw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIiNiNJInRHRipGLiwkKiZJImhHRiohIiMsJi0mRik2IyIiI0YtI0Y3IiIkRicjRjJGOUYsJEY3ISIm</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCQqKCRGJyEiJiIiIilJImhHRiVGJyEiIiwoLSZGLzYjRjZGMEY2KiZGJ0Y2Ri1GNkY5LSZGLzYjIiIkRjBGNkY2RjY=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIjNiNJInRHRipGLiwkKiZJImhHRiohIiMsKC0mRik2IyIiIkYtRjdGJ0YyLSZGKTYjIiIkRi1GN0Y3JEYsISIm</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCQqKCQiIiMhIiYiIiIpSSJoR0YlRjUhIiIsKC0mRi82I0Y1RjBGNyomRjVGN0YtRjdGOi0mRi82IyIiJUYwRjdGN0Y3">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIkNiNJInRHRipGLiwkKiZJImhHRiohIiMsKC0mRik2IyIiI0YtIiIiRidGMi0mRik2IyIiJUYtRjhGOCRGNyEiJg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCQqKCQiIiMhIiYiIiIpSSJoR0YlRjUhIiIsKC0mRi82IyIiJEYwRjcqJkY1RjdGLUY3RjotJkYvNiMiIiZGMEY3RjdGNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIlNiNJInRHRipGLiwkKiZJImhHRiohIiMsKC0mRik2IyIiJEYtIiIiRidGMi0mRik2IyIiJkYtRjhGOCQiIiMhIiY=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiYvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCQqKCQiIiMhIiYiIiIpSSJoR0YlRjUhIiIsKC0mRi82IyIiJUYwRjcqJkY1RjdGLUY3RjotJkYvNiMiIidGMEY3RjdGNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiImNiNJInRHRipGLiwkKiZJImhHRiohIiMsKC0mRik2IyIiJUYtIiIiRidGMi0mRik2IyIiJ0YtRjhGOCQiIiMhIiY=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIicvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCQqKCQiIiMhIiYiIiIpSSJoR0YlRjUhIiIsKC0mRi82IyIiJkYwRjcqJkY1RjdGLUY3RjotJkYvNiMiIihGMEY3RjdGNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiInNiNJInRHRipGLiwkKiZJImhHRiohIiMsKC0mRik2IyIiJkYtIiIiRidGMi0mRik2IyIiKEYtRjhGOCQiIiMhIiY=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIigvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCQqKCQiIiMhIiYiIiIpSSJoR0YlRjUhIiIsKC0mRi82IyIiJ0YwRjcqJkY1RjdGLUY3RjotJkYvNiMiIilGMEY3RjdGNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIoNiNJInRHRipGLiwkKiZJImhHRiohIiMsKC0mRik2IyIiJ0YtIiIiRidGMi0mRik2IyIiKUYtRjhGOCQiIiMhIiY=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIikvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCQqKCQiIiMhIiYiIiIpSSJoR0YlRjUhIiIsKC0mRi82IyIiKEYwRjcqJkY1RjdGLUY3RjotJkYvNiMiIipGMEY3RjdGNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIpNiNJInRHRipGLiwkKiZJImhHRiohIiMsKC0mRik2IyIiKEYtIiIiRidGMi0mRik2IyIiKkYtRjhGOCQiIiMhIiY=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiovLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCQqKCQiIiMhIiYiIiIpSSJoR0YlRjUhIiIsKC0mRi82IyIiKUYwRjcqJkY1RjdGLUY3RjotJkYvNiMiIzVGMEY3RjdGNw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIqNiNJInRHRipGLiwkKiZJImhHRiohIiMsKC0mRik2IyIiKUYtIiIiRidGMi0mRik2IyIjNUYtRjhGOCQiIiMhIiY=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIzUvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCQqKCQiIiMhIiYiIiIpSSJoR0YlRjUhIiIsJi0mRi82IyIiKkYwRjcqJkY1RjdGLUY3RjpGN0Y3">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiM1NiNJInRHRipGLiwkKiZJImhHRiohIiMsJi0mRik2IyIiKkYtIiIiRidGMkY4JCIiIyEiJg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=[seq(rhs(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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">NywsJComSSJoRzYiISIjLCYtJkkidUdGJjYjIiIjNiNJInRHRiYjRi0iIiQtJkYrNiMiIiJGLiNGJ0YxRjUkRi0hIiYsJComRiVGJywoRjJGNUYpRictJkYrNiNGMUYuRjVGNUY3LCQqJkYlRicsKEYpRjVGPEYnLSZGKzYjIiIlRi5GNUY1RjcsJComRiVGJywoRjxGNUZCRictJkYrNiMiIiZGLkY1RjVGNywkKiZGJUYnLChGQkY1RklGJy0mRis2IyIiJ0YuRjVGNUY3LCQqJkYlRicsKEZJRjVGUEYnLSZGKzYjIiIoRi5GNUY1RjcsJComRiVGJywoRlBGNUZXRictJkYrNiMiIilGLkY1RjVGNywkKiZGJUYnLChGV0Y1RmhuRictJkYrNiMiIipGLkY1RjVGNywkKiZGJUYnLChGaG5GNUZfb0YnLSZGKzYjIiM1Ri5GNUY1RjcsJComRiVGJywmRl9vRjVGZm9GJ0Y1Rjc=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" 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="PkkiWUc2IjcsLSZJInVHRiQ2IyIiIjYjSSJ0R0YkLSZGKDYjIiIjRistJkYoNiMiIiRGKy0mRig2IyIiJUYrLSZGKDYjIiImRistJkYoNiMiIidGKy0mRig2IyIiKEYrLSZGKDYjIiIpRistJkYoNiMiIipGKy0mRig2IyIjNUYr">NywtJkkidUc2IjYjIiIiNiNJInRHRiYtJkYlNiMiIiNGKS0mRiU2IyIiJEYpLSZGJTYjIiIlRiktJkYlNiMiIiZGKS0mRiU2IyIiJ0YpLSZGJTYjIiIoRiktJkYlNiMiIilGKS0mRiU2IyIiKkYpLSZGJTYjIiM1Rik=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=genmatrix(eqs,Y);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQUc2Ii1JJ21hdHJpeEdGJDYjNyw3LCwkKiYkIitMTExMOCEjOSIiIilJImhHRiQiIiMhIiJGMywkRitGLyIiIUY1RjVGNUY1RjVGNUY1NywsJComJEYyISImRi9GMEYzRi8sJComJCIiJUY6Ri9GMEYzRjNGN0Y1RjVGNUY1RjVGNUY1NyxGNUY3RjtGN0Y1RjVGNUY1RjVGNTcsRjVGNUY3RjtGN0Y1RjVGNUY1RjU3LEY1RjVGNUY3RjtGN0Y1RjVGNUY1NyxGNUY1RjVGNUY3RjtGN0Y1RjVGNTcsRjVGNUY1RjVGNUY3RjtGN0Y1RjU3LEY1RjVGNUY1RjVGNUY3RjtGN0Y1NyxGNUY1RjVGNUY1RjVGNUY3RjtGNzcsRjVGNUY1RjVGNUY1RjVGNUY3Rjs=">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">h:=eval(L/(N+1));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiaEc2IiQiKz09PT09ISM3">JCIrPT09PT0hIzc=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=map(eval,A);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQUc2Ii1JJ21hdHJpeEdGJDYjNyw3LCQhK01MTExTISIqJCIrTUxMTFNGLCIiIUYvRi9GL0YvRi9GL0YvNywkIistKytdZ0YsJCErKysrNTchIilGMUYvRi9GL0YvRi9GL0YvNyxGL0YxRjNGMUYvRi9GL0YvRi9GLzcsRi9GL0YxRjNGMUYvRi9GL0YvRi83LEYvRi9GL0YxRjNGMUYvRi9GL0YvNyxGL0YvRi9GL0YxRjNGMUYvRi9GLzcsRi9GL0YvRi9GL0YxRjNGMUYvRi83LEYvRi9GL0YvRi9GL0YxRjNGMUYvNyxGL0YvRi9GL0YvRi9GL0YxRjNGMTcsRi9GL0YvRi9GL0YvRi9GL0YxRjM=">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">if N &gt; 4 then A:=map(evalf,A);end: </Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalm(A);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUknbWF0cml4RzYiNiM3LDcsJCErTUxMTFMhIiokIitNTExMU0YqJCIiIUYuRi1GLUYtRi1GLUYtRi03LCQiKy0rK11nRiokISsrKys1NyEiKUYwRi1GLUYtRi1GLUYtRi03LEYtRjBGMkYwRi1GLUYtRi1GLUYtNyxGLUYtRjBGMkYwRi1GLUYtRi1GLTcsRi1GLUYtRjBGMkYwRi1GLUYtRi03LEYtRi1GLUYtRjBGMkYwRi1GLUYtNyxGLUYtRi1GLUYtRjBGMkYwRi1GLTcsRi1GLUYtRi1GLUYtRjBGMkYwRi03LEYtRi1GLUYtRi1GLUYtRjBGMkYwNyxGLUYtRi1GLUYtRi1GLUYtRjBGMg==">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=exponential(A,t):</Text-field>
</Input>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=map(evalf,mat):</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y0:=matrix(N,1):for i from 1 to N do Y0[i,1]:=evalf(subs(x=i*h,rhs(IC)));od:evalm(Y0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUknbWF0cml4RzYiNiM3LDcjJCIrPldAKSopKiEjNTcjJCIrTyhIXGYqRio3IyQiK2AqPmo0KkYqNyMkIitHYGA3JSlGKjcjJCIrWGRcZHZGKjcjJCIrUHRnW2xGKjcjJCIrdCIza1MmRio3IyQiK04sOmFURio3IyQiK2xiSzxHRio3IyQiKyFRW0pVIkYq">PTYiNiQ7IiIiIiM1O0YmRiZFXFtsKzYkIiImRiYkIitYZFxkdiEjNTYkIiIlRiYkIitHYGA3JSlGLjYkRidGJiQiKyFRW0pVIkYuNiQiIipGJiQiK2xiSzxHRi42JCIiKEYmJCIrdCIza1MmRi42JCIiI0YmJCIrTyhIXGYqRi42JEYmRiYkIis+V0ApKikqRi42JCIiJ0YmJCIrUHRnW2xGLjYkIiIpRiYkIitOLDphVEYuNiQiIiRGJiQiK2AqPmo0KkYu</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=evalm(mat&amp;*Y0):</Text-field>
</Input>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=map(simplify,Y);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PTYiNiQ7IiIiIiM1O0YmRiZFXFtsKzYkIiImRiYsNi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGIzYjLCRJInRHRiMkIStYZGlqQiEiKSQiJlg1JSEjNi1GLjYjLCRGNCQhKypHVyoqPiNGNyQiJTl4ISM3LUYuNiMsJEY0JCErOyx0Vz5GNyQhJjwhKilGOi1GLjYjLCRGNCQhK0gxXEE7RjckISc1KmYjRjotRi42IywkRjQkISszSSZSRSJGNyQiJz4pbyJGOi1GLjYjLCRGNCQhK0pXXEchKiEiKiQiJiRIeCEjNS1GLjYjLCRGNCQhKzxxckFkRmduJCInNWJKRjotRi42IywkRjQkISs2VWg0SUZnbiQhKDRYLyRGOi1GLjYjLCRGNCQhK2lpeiw2RmduJCEoa2N4JkY6LUYuNiMsJEY0JCErZGF0SzdGam4kIis4TkdldkZqbjYkIiIlRiYsNkYtJCEmeC4kRjpGOyQhJl1IIkZqbkZDJCEmbUUlRkJGSiQiJ2NnOkY6RlEkIiZaWCVGam5GWCQiJ0YkKT5GOkZbbyQhKFFFISoqRkJGYm8kISduKDQkRmpuRmlvJCEpO25UOUZCRmBwJCIrR18tOCUpRmpuNiRGJ0YmLDZGLSQhJjdKIkY6RjskIiZkNSVGOkZDJCEnaHE2RjpGSiQiJyJ5QCNGOkZRJCEmLjAlRmpuRlgkIid4Kj0oRjpGW28kISg/cT4iRjpGYm8kIih4LDcjRjpGaW8kIShXXl0lRjpGYHAkIitnMllCOUZqbjYkIiIqRiYsNkYtJCImIVFARjpGOyQhJXMpKkZqbkZDJCInMT06RjpGSiQhJ1tRPUY6RlEkIiYmKSpmRjpGWCQiJ0NDUUY6RltvJCEnaGI3RmpuRmJvJCInUHpKRmpuRmlvJCEobjk+KUY6RmBwJCIrNnUieiJHRmpuNiQiIihGJiw2Ri0kIidGJHkkRkJGOyQhJSJRKUZqbkZDJCEmJltsRjpGSiQiJisvI0ZqbkZRJCEoIj5qQCEjOEZYJCEmdCZlRmpuRltvJCIobSFlNkY6RmJvJCInRnR4RjpGaW8kIShYJ3A1RmpuRmBwJCIrP2NMMmFGam42JCIiI0YmLDZGLSQhJiRHOEY6RjskISdLbTVGOkZDJCEnU3M3RjpGSiQhJ1JqREY6RlEkISgieldORkJGWCQhJy0rW0Y6RltvJCEnTjpPRjpGYm8kIicxW2pGOkZpbyQiKFc/PChGOkZgcCQiK3khPlZmKkZqbjYkRiZGJiw2Ri0kIiV1UUY6RjskISYkM0VGOkZDJCImUVAlRjpGSiQiJlxRKUY6RlEkIidCTj9GOkZYJCInOThTRjpGW28kIiYoNCgqRmpuRmJvJCIoTyRvREY6RmlvJCIpdSMqeikqRkJGYHAkIissOyFvKikqRmpuNiQiIidGJiw2Ri0kISVRUUZqbkY7JCEmUSVHRjpGQyQiJypRayJGOkZKJCEnJGZvKUZCRlEkISc8YU1GOkZYJCInSTBERjpGW28kIic7ajhGam5GYm8kIShPZ1wiRjpGaW8kISh3JWYhKkY6RmBwJCIrSGNgXGxGam42JCIiKUYmLDZGLSQhJlBJJEY6RjskIiVeaEZqbkZDJCEmbipbRjpGSiQhJyNRZiJGOkZRJCImNF0lRmpuRlgkISYhPVxGam5GW28kIScoMzgiRjpGYm8kIidgV0VGam5GaW8kIShhKVE1RmpuRmBwJCIrKXljXDolRmpuNiQiIiRGJiw2Ri0kIiYpNEdGOkY7JCIlak1Gam5GQyQiJnZaIkZqbkZKJCImIXBuRjpGUSQhKE9xMiJGQkZYJCEnQ1VpRjpGW28kISdGPThGam5GYm8kIShXemkiRjpGaW8kIigwTzokRjpGYHAkIit6Wk0nNCpGam4=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N do u[i](t):=evalf((Y[i,1]));od:</Text-field>
</Input>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 do u[i](t):=eval(u[i](t));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErWGRpakIhIikkIisrKyskZiohIzwtRiQ2IywkRiskISsqR1cqKj4jRi4kIilubW13ISM7LUYkNiMsJEYrJCErOyx0Vz5GLiQiK25tSTI1ISM6LUYkNiMsJEYrJCErSDFcQTtGLiQiKysrWHM+RkEtRiQ2IywkRiskISszSSZSRSJGLiQiKytxQiYqUUZBLUYkNiMsJEYrJCErSldcRyEqISIqJCIrKysnMyZwRkEtRiQ2IywkRiskISs8cXJBZEZVJCIrTSRRXlQiISM5LUYkNiMsJEYrJCErNlVoNElGVSQiKytnJUdAJEZpbi1GJDYjLCRGKyQhK2lpeiw2RlUkIis/YkR5NSEjOC1GJDYjLCRGKyQhK2RhdEs3ISM1JCIrNiJIdyoqKkZecA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErWGRpakIhIikkIiV1USEjNi1GJDYjLCRGKyQhKypHVyoqPiNGLiQhJiQzRUYxLUYkNiMsJEYrJCErOyx0Vz5GLiQiJlFQJUYxLUYkNiMsJEYrJCErSDFcQTtGLiQiJlxRKUYxLUYkNiMsJEYrJCErM0kmUkUiRi4kIidCTj9GMS1GJDYjLCRGKyQhK0pXXEchKiEiKiQiJzk4U0YxLUYkNiMsJEYrJCErPHFyQWRGUyQiJig0KCohIzUtRiQ2IywkRiskISs2VWg0SUZTJCIoTyRvREYxLUYkNiMsJEYrJCEraWl6LDZGUyQiKXUjKnopKiEjNy1GJDYjLCRGKyQhK2RhdEs3RmduJCIrLDshbyopKkZnbg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErWGRpakIhIikkISYkRzghIzYtRiQ2IywkRiskISsqR1cqKj4jRi4kISdLbTVGMS1GJDYjLCRGKyQhKzssdFc+Ri4kISdTczdGMS1GJDYjLCRGKyQhK0gxXEE7Ri4kISdSakRGMS1GJDYjLCRGKyQhKzNJJlJFIkYuJCEoInpXTiEjNy1GJDYjLCRGKyQhK0pXXEchKiEiKiQhJy0rW0YxLUYkNiMsJEYrJCErPHFyQWRGVCQhJ046T0YxLUYkNiMsJEYrJCErNlVoNElGVCQiJzFbakYxLUYkNiMsJEYrJCEraWl6LDZGVCQiKFc/PChGMS1GJDYjLCRGKyQhK2RhdEs3ISM1JCIreSE+VmYqRltw</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiQ2I0kidEdGJiw2KiYkIiYpNEchIzYiIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IywkKiYkIitYZGlqQiEiKUYwRipGMCEiIkYwRjAqJiQiJWpNISM1RjAtRjI2IywkKiYkIisqR1cqKj4jRjtGMEYqRjBGPEYwRjAqJiQiJnZaIkZARjAtRjI2IywkKiYkIis7LHRXPkY7RjBGKkYwRjxGMEYwKiYkIiYhcG5GL0YwLUYyNiMsJComJCIrSDFcQTtGO0YwRipGMEY8RjBGMComJCIoT3EyIiEjN0YwLUYyNiMsJComJCIrM0kmUkUiRjtGMEYqRjBGPEYwRjwqJiQiJ0NVaUYvRjAtRjI2IywkKiYkIitKV1xHISohIipGMEYqRjBGPEYwRjwqJiQiJ0Y9OEZARjAtRjI2IywkKiYkIis8cXJBZEZmb0YwRipGMEY8RjBGPComJCIoV3ppIkYvRjAtRjI2IywkKiYkIis2VWg0SUZmb0YwRipGMEY8RjBGPComJCIoME86JEYvRjAtRjI2IywkKiYkIitpaXosNkZmb0YwRipGMEY8RjBGMComJCIrelpNJzQqRkBGMC1GMjYjLCQqJiQiK2RhdEs3RkBGMEYqRjBGPEYwRjA=">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErWGRpakIhIikkIiYpNEchIzYtRiQ2IywkRiskISsqR1cqKj4jRi4kIiVqTSEjNS1GJDYjLCRGKyQhKzssdFc+Ri4kIiZ2WiJGOS1GJDYjLCRGKyQhK0gxXEE7Ri4kIiYhcG5GMS1GJDYjLCRGKyQhKzNJJlJFIkYuJCEoT3EyIiEjNy1GJDYjLCRGKyQhK0pXXEchKiEiKiQhJ0NVaUYxLUYkNiMsJEYrJCErPHFyQWRGVSQhJ0Y9OEY5LUYkNiMsJEYrJCErNlVoNElGVSQhKFd6aSJGMS1GJDYjLCRGKyQhK2lpeiw2RlUkIigwTzokRjEtRiQ2IywkRiskIStkYXRLN0Y5JCIrelpNJzQqRjk=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErWGRpakIhIikkISZ4LiQhIzYtRiQ2IywkRiskISsqR1cqKj4jRi4kISZdSCIhIzUtRiQ2IywkRiskISs7LHRXPkYuJCEmbUUlISM3LUYkNiMsJEYrJCErSDFcQTtGLiQiJ2NnOkYxLUYkNiMsJEYrJCErM0kmUkUiRi4kIiZaWCVGOS1GJDYjLCRGKyQhK0pXXEchKiEiKiQiJ0YkKT5GMS1GJDYjLCRGKyQhKzxxckFkRlUkIShRRSEqKkZBLUYkNiMsJEYrJCErNlVoNElGVSQhJ24oNCRGOS1GJDYjLCRGKyQhK2lpeiw2RlUkISk7blQ5RkEtRiQ2IywkRiskIStkYXRLN0Y5JCIrR18tOCUpRjk=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErWGRpakIhIikkIiZYNSUhIzYtRiQ2IywkRiskISsqR1cqKj4jRi4kIiU5eCEjNy1GJDYjLCRGKyQhKzssdFc+Ri4kISY8ISopRjEtRiQ2IywkRiskIStIMVxBO0YuJCEnNSpmI0YxLUYkNiMsJEYrJCErM0kmUkUiRi4kIic+KW8iRjEtRiQ2IywkRiskIStKV1xHISohIiokIiYkSHghIzUtRiQ2IywkRiskISs8cXJBZEZUJCInNWJKRjEtRiQ2IywkRiskISs2VWg0SUZUJCEoNFgvJEYxLUYkNiMsJEYrJCEraWl6LDZGVCQhKGtjeCZGMS1GJDYjLCRGKyQhK2RhdEs3RlckIis4TkdldkZX</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErWGRpakIhIikkISVRUSEjNS1GJDYjLCRGKyQhKypHVyoqPiNGLiQhJlElRyEjNi1GJDYjLCRGKyQhKzssdFc+Ri4kIicqUWsiRjktRiQ2IywkRiskIStIMVxBO0YuJCEnJGZvKSEjNy1GJDYjLCRGKyQhKzNJJlJFIkYuJCEnPGFNRjktRiQ2IywkRiskIStKV1xHISohIiokIidJMERGOS1GJDYjLCRGKyQhKzxxckFkRlUkIic7ajhGMS1GJDYjLCRGKyQhKzZVaDRJRlUkIShPZ1wiRjktRiQ2IywkRiskIStpaXosNkZVJCEodyVmISpGOS1GJDYjLCRGKyQhK2RhdEs3RjEkIitIY2BcbEYx</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErWGRpakIhIikkIidGJHkkISM3LUYkNiMsJEYrJCErKkdXKio+I0YuJCElIlEpISM1LUYkNiMsJEYrJCErOyx0Vz5GLiQhJiZbbCEjNi1GJDYjLCRGKyQhK0gxXEE7Ri4kIiYrLyNGOS1GJDYjLCRGKyQhKzNJJlJFIkYuJCEoIj5qQCEjOC1GJDYjLCRGKyQhK0pXXEchKiEiKiQhJnQmZUY5LUYkNiMsJEYrJCErPHFyQWRGViQiKG0hZTZGQS1GJDYjLCRGKyQhKzZVaDRJRlYkIidGdHhGQS1GJDYjLCRGKyQhK2lpeiw2RlYkIShYJ3A1RjktRiQ2IywkRiskIStkYXRLN0Y5JCIrP2NMMmFGOQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErWGRpakIhIikkISZQSSQhIzYtRiQ2IywkRiskISsqR1cqKj4jRi4kIiVeaCEjNS1GJDYjLCRGKyQhKzssdFc+Ri4kISZuKltGMS1GJDYjLCRGKyQhK0gxXEE7Ri4kIScjUWYiRjEtRiQ2IywkRiskISszSSZSRSJGLiQiJjRdJUY5LUYkNiMsJEYrJCErSldcRyEqISIqJCEmIT1cRjktRiQ2IywkRiskISs8cXJBZEZUJCEnKDM4IkYxLUYkNiMsJEYrJCErNlVoNElGVCQiJ2BXRUY5LUYkNiMsJEYrJCEraWl6LDZGVCQhKGEpUTVGOS1GJDYjLCRGKyQhK2RhdEs3RjkkIispeWNcOiVGOQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErWGRpakIhIikkIiYhUUAhIzYtRiQ2IywkRiskISsqR1cqKj4jRi4kISVzKSohIzUtRiQ2IywkRiskISs7LHRXPkYuJCInMT06RjEtRiQ2IywkRiskIStIMVxBO0YuJCEnW1E9RjEtRiQ2IywkRiskISszSSZSRSJGLiQiJiYpKmZGMS1GJDYjLCRGKyQhK0pXXEchKiEiKiQiJ0NDUUYxLUYkNiMsJEYrJCErPHFyQWRGVCQhJ2hiN0Y5LUYkNiMsJEYrJCErNlVoNElGVCQiJ1B6SkY5LUYkNiMsJEYrJCEraWl6LDZGVCQhKG45PilGMS1GJDYjLCRGKyQhK2RhdEs3RjkkIis2dSJ6IkdGOQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ0R0YoJCErWGRpakIhIikkISY3SiIhIzYtRiQ2IywkRiskISsqR1cqKj4jRi4kIiZkNSVGMS1GJDYjLCRGKyQhKzssdFc+Ri4kISdocTZGMS1GJDYjLCRGKyQhK0gxXEE7Ri4kIicieUAjRjEtRiQ2IywkRiskISszSSZSRSJGLiQhJi4wJSEjNS1GJDYjLCRGKyQhK0pXXEchKiEiKiQiJ3gqPShGMS1GJDYjLCRGKyQhKzxxckFkRlQkISg/cT4iRjEtRiQ2IywkRiskISs2VWg0SUZUJCIoeCw3I0YxLUYkNiMsJEYrJCEraWl6LDZGVCQhKFdeXSVGMS1GJDYjLCRGKyQhK2RhdEs3Rk4kIitnMllCOUZO</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIzY2I0kidEdGJiIiIQ==">IiIh</Equation></Text-field>
</Output>
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<Group labelreference="L37" 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="L38" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Set the color list:</Text-field>
</Input>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">setcolors([&quot;Red&quot;, &quot;Blue&quot;, &quot;LimeGreen&quot;, &quot;Goldenrod&quot;, &quot;maroon&quot;, &quot;DarkTurquoise&quot;, &quot;coral&quot;, &quot;aquamarine&quot;, &quot;magenta&quot;, &quot;khaki&quot;,  &quot;sienna&quot;, &quot;orange&quot;, &quot;yellow&quot;, &quot;gray&quot;]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyhRJFJlZDYiUSpMaW1lR3JlZW5GJFEqR29sZGVucm9kRiRRJUJsdWVGJFEtTWVkaXVtT3JjaGlkRiRRLkRhcmtUdXJxdW9pc2VGJA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pp:=plot([seq(u[i](t),i=0..N+1)],t=0..tf,thickness=3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 16696 characters]">[encoded data, 16640 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Plot the texts:</Text-field>
</Input>
</Group>
<Group labelreference="L54" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">arw:=arrow(&lt;6.0,0.55&gt;,&lt;-5.0,-0.57&gt;,width=[1/1000,relative=true],head_width=[1/50,relative=false],head_length=[1/5,relative=false]):
pt:=textplot([[11,0.6,typeset(&quot;Follow the arrow: &quot;,u[0],&quot;(t), ..., &quot;,u[N+1],&quot;(t).&quot;)]]):</Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display([pp,pt,arw],title=&quot;Figure Exp. 5.25.&quot;,axes=boxed,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, 33116 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L40" 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="L41" 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="L42" 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="PkkjVDFHNiI3QSIiISMiIiMiIiQjIiIlRilGKCMiIilGKSMiIzVGKUYrIyIjOUYpIyIjO0YpIiInIyIjP0YpIyIjQUYpRi0jIiNFRikjIiNHRilGLyMiI0tGKSMiI01GKSIjNyMiI1FGKSMiI1NGKUYxIyIjV0YpIyIjWUYpRjMjIiNdRikjIiNfRikiIz0jIiNjRikjIiNlRilGNg==">N0EiIiEjIiIjIiIkIyIiJUYmRiUjIiIpRiYjIiM1RiZGKCMiIzlGJiMiIztGJiIiJyMiIz9GJiMiI0FGJkYqIyIjRUYmIyIjR0YmRiwjIiNLRiYjIiNNRiYiIzcjIiNRRiYjIiNTRiZGLiMiI1dGJiMiI1lGJkYwIyIjXUYmIyIjX0YmIiM9IyIjY0YmIyIjZUYmRjM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L43" 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="L44" 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="L45" 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="L46" 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="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">surfdata(plotdata,axes=boxed,title=&quot;Figure 5.26.&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, 17120 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>