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<Task>
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<Group labelreference="L69" drawlabel="true">
<Input>
<Text-field style="Heading 3" layout="Heading 3"><Font italic="false">Example 5.10</Font></Text-field>
</Input>
</Group>
<Group labelreference="L68" 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(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);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZ2VHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkidEdGJEYuLCQtRic2JEYqRi0hIiI=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLCwkLUYkNiRGJ0YrISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=u(x,t)-1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLCYtSSJ1R0YkNiRJInhHRiRJInRHRiQiIiJGKyEiIg==">LCYtSSJ1RzYiNiRJInhHRiVJInRHRiUiIiIhIiJGKQ==</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),t)=-diff(u(x,t),x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1R0YkNiRJInhHRiRJInRHRiRGLiwkLUYnNiRGKkYtISIi">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLCwkLUYkNiRGJ0YrISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IC:=u(x,0)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSUNHNiIvLUkidUdGJDYkSSJ4R0YkIiIhRio=">Ly1JInVHNiI2JEkieEdGJSIiIUYo</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTkc2IiIiIw==">IiIj</Equation></Text-field>
</Output>
</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>
</Output>
</Group>
<Group labelreference="L10" 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>
</Group>
<Group labelreference="L11" 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>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxb:=(u[N+1](t)-u[N](t))/h:</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydx:=1/h*(u[m](t)-u[m-1](t)):</Text-field>
</Input>
</Group>
<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>
</Group>
<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>
</Group>
<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>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[0]:=bc1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiEsJi0mSSJ1R0YlRiY2I0kidEdGJSIiIkYuISIi">LCYtJkkidUc2IjYjIiIhNiNJInRHRiYiIiIhIiJGKw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[N+1]:=bc2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCQqJiwmRi0iIiItJkYvNiMiIiNGMCEiIkY1SSJoR0YlRjpGOg==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIkNiNJInRHRipGLiwkKiYsJkYnIiIiLSZGKTYjIiIjRi0hIiJGMkkiaEdGKkY3Rjc=</Equation></Text-field>
</Output>
</Group>
<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>
</Input>
</Group>
<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>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N+1 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="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCQqJkkiaEdGJSEiIiwmRi1GJ0YnRjVGJ0Y1">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIiNiNJInRHRipGLiwkKiZJImhHRiohIiIsJkYnRixGMkYsRixGMg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCQqJkkiaEdGJSEiIiwmRi0iIiItJkYvNiNGN0YwRjVGN0Y1">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIjNiNJInRHRipGLiwkKiZJImhHRiohIiIsJkYnIiIiLSZGKTYjRjRGLUYyRjRGMg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJ1R0YlRiY2I0kidEdGJUYxLCQqJiwmRi0iIiItJkYvNiMiIiNGMCEiIkY1SSJoR0YlRjpGOg==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkidUc2IjYjIiIkNiNJInRHRipGLiwkKiYsJkYnIiIiLSZGKTYjIiIjRi0hIiJGMkkiaEdGKkY3Rjc=</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+1)]:</Text-field>
</Input>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=[seq(u[i](t),i=1..N+1)]:</Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=genmatrix(eqs,Y,'b1'):</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b:=matrix(N+1,1):for i to N+1 do b[i,1]:=-eval(b1[i]);od:evalm(b):</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">h:=eval(L/(N+1)):</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=map(eval,A):</Text-field>
</Input>
</Group>
<Group labelreference="L29" 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="L30" 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="LUknbWF0cml4RzYiNiM3JTclISIkIiIhRik3JSIiJEYoRik3JUYpRitGKA==">PTYiNiQ7IiIiIiIkRiVFXFtsKjYkIiIjRiZGJzYkRiZGJyIiITYkRiZGKkYsNiRGKkYqISIkNiRGJ0YmRiw2JEYnRipGJzYkRipGJ0YsNiRGJ0YnRi82JEYmRiZGLw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">J:=jordan(A,S);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiSkc2Ii1JJ21hdHJpeEdGJDYjNyU3JSEiJCIiIiIiITclRixGKkYrNyVGLEYsRio=">PTYiNiQ7IiIiIiIkRiVFXFtsKjYkIiIjRiYiIiE2JEYmRidGKzYkRiZGKkYmNiRGKkYqISIkNiRGJ0YmRis2JEYnRipGKzYkRipGJ0YmNiRGJ0YnRi82JEYmRiZGLw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalm(S);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUknbWF0cml4RzYiNiM3JTclIiIhRigiIiI3JUYoIiIkRig3JSIiKkYoRig=">PTYiNiQ7IiIiIiIkRiVFXFtsKjYkIiIjRiYiIiE2JEYmRidGJjYkRiZGKkYrNiRGKkYqRic2JEYnRiYiIio2JEYnRipGKzYkRipGJ0YrNiRGJ0YnRis2JEYmRiZGKw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=evalm(S&amp;*exponential(J,t)&amp;*inverse(S));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkbWF0RzYiLUknbWF0cml4R0YkNiM3JTclLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComIiIkIiIiSSJ0R0YkRjMhIiIiIiFGNjclLCQqKEYyRjNGNEYzRipGM0YzRipGNjclLCQqKCMiIioiIiNGMylGNEY/RjNGKkYzRjNGOEYq">PTYiNiQ7IiIiIiIkRiVFXFtsKjYkIiIjRiYsJComSSJ0R0YjRiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiM2IywkRi0hIiRGJkYnNiRGJkYnIiIhNiRGJkYqRjc2JEYqRipGLjYkRidGJiwkKiZGLUYqRi5GJiMiIipGKjYkRidGKkYrNiRGKkYnRjc2JEYnRidGLjYkRiZGJkYu</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Nrow:=rowdim(A):</Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">l:=evalf(eigenvalues(A));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkibEc2IjYlJCEiJCIiIUYmRiY=">NiUkISIkIiIhRiNGIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> </Text-field>
</Input>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to Nrow do lambda[i]:=l[i];od:</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Id:=Matrix(Nrow,Nrow,shape=identity):</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">X:=matrix(Nrow,1,[seq(beta[i],i=1..Nrow)]):</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for k to Nrow do:</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">G:=evalm((A-lambda[k]*Id)&amp;*X):</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqx[1]:=beta[1]=1:for i from 2 to Nrow do eqx[i]:=G[i-1,1]:od:</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to Nrow do beta[i]:=solve(eqx[i],beta[i]);od:</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">XX[k]:=map(eval,evalm(X)):</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to Nrow do unassign('beta[i]'):od:od:</Text-field>
</Input>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> </Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P:=Matrix([seq(evalm(XX[i]),i=1..Nrow)]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiUEc2Ii1JJ1JUQUJMRUdGJDYlIiohW0tKOi1JJ01BVFJJWEdGJDYjNyU3JSIiIkYuRi43JSZJJWJldGFHRiQ2IyIiI0YwRjA3JUklTlVMTEclKnByb3RlY3RlZEdGNUY1SSdNYXRyaXhHNiRGNkkoX3N5c2xpYkdGJA==">LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKiFbS0o6</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">expD1:=Matrix(1..Nrow,1..Nrow,shape=diagonal):</Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to Nrow do expD1[i,i]:=exp(lambda[i]*t):od:</Text-field>
</Input>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">expD1:=map(convert,expD1,trig):</Text-field>
</Input>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=evalm(P&amp;*expD1&amp;*inverse(P)):</Text-field>
</Input>
<Output>
<Text-field style="Error" layout="Error">Error, (in evalm) unnamed vector or array with undefined entries.</Text-field>
</Output>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=map(expand,mat):</Text-field>
</Input>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=map(simplify,mat):</Text-field>
</Input>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y0:=matrix(N+1,1):for i from 1 to N+1 do Y0[i,1]:=evalf(subs(x=i*h,rhs(IC)));od:evalm(Y0):</Text-field>
</Input>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=evalm(mat&amp;*(Y0+inverse(A)&amp;*b)-inverse(A)&amp;*b):</Text-field>
</Input>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">#b2:=subs(t=tau,evalm(b)):</Text-field>
</Input>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">#mat2:=subs(t=t-tau,evalm(mat)):</Text-field>
</Input>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">#mat3:=evalm(mat2&amp;*b2):</Text-field>
</Input>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">#mat4:=map(int,mat3,tau=0..t):</Text-field>
</Input>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">#Y:=evalm(mat&amp;*Y0+mat4):</Text-field>
</Input>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N+1 do u[i](t):=evalf((Y[i,1]));od:</Text-field>
</Input>
</Group>
<Group labelreference="L54" 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>
</Group>
<Group labelreference="L55" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 do u[i](t):=subs(I=0,u[i](t));od:</Text-field>
</Input>
</Group>
<Group labelreference="L71" 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>
</Group>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pp:=plot([seq(subs(delta=1,u[i](t)),i=0..N+1)],t=0..1,thickness=4);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 5520 characters]">[encoded data, 5488 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L70" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pt:=textplot([seq([0.4,evalf(subs(delta=1,t=0.4,u[i](t))),typeset(u[i],&quot;(t)&quot;),align={below,right}],i=0..N+1)]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjcHRHNiItSS9JTlRFUkZBQ0VfUExPVEdGJDYmLUklVEVYVEdGJDYmNyQkIiIlISIiJCIiIiIiIS1JKV9UWVBFU0VUR0YkNiQmSSJ1R0YkNiNGMVEkKHQpRiRJK0FMSUdOQkVMT1dHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiRJK0FMSUdOUklHSFRHRjotRik2JjckRiwkIisiKXkwKSlwISM1LUYzNiQmRjY2I0YwRjhGOUY9LUYpNiY3JEYsJCIrUXRzdExGQy1GMzYkJkY2NiMiIiNGOEY5Rj0tRik2JjckRiwkIis4IUhePyJGQy1GMzYkJkY2NiMiIiRGOEY5Rj0=">LSUlUExPVEc2Ji1JJVRFWFRHNiI2JjckJCIiJSEiIiQiIiIiIiEtSSlfVFlQRVNFVEdGJzYkJkkidUdGJzYjRi9RJCh0KUYnSStBTElHTkJFTE9XRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YnSStBTElHTlJJR0hUR0Y4LUYmNiY3JEYqJCIrIil5MCkpcCEjNS1GMTYkJkY0NiNGLkY2RjdGOy1GJjYmNyRGKiQiK1F0c3RMRkEtRjE2JCZGNDYjIiIjRjZGN0Y7LUYmNiY3JEYqJCIrOCFIXj8iRkEtRjE2JCZGNDYjIiIkRjZGN0Y7</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display([pp,pt],title=&quot;Figure Exp. 5.32.&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, 20220 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L58" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 do p[i]:=plot(subs(delta=0.1,u[i](t)),t=0..0.4,thickness=3);od:</Text-field>
</Input>
</Group>
<Group labelreference="L59" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tf:=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdGZHNiIiIiI=">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L60" 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="L61" 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="PkkjVDFHNiI3QSIiISMiIiIiI0kjRigiIzojRigiIzUjIiIjRisjRigiIicjRigiIiYjIiIoRikjIiIlRisjIiIkRi0jRihGOSMiIzZGKSNGL0YzIyIjOEYpI0Y1RisjRihGLyMiIilGKyMiIzxGKSNGOUYzIyIjPkYpI0YvRjkjRjVGLSNGPEYrIyIjQkYpI0Y3RjMjRjNGMSNGP0YrIyIiKkYtIyIjOUYrIyIjSEYpRig=">N0EiIiEjIiIiIiNJI0YlIiM6I0YlIiM1IyIiI0YoI0YlIiInI0YlIiImIyIiKEYmIyIiJUYoIyIiJEYqI0YlRjYjIiM2RiYjRixGMCMiIzhGJiNGMkYoI0YlRiwjIiIpRigjIiM8RiYjRjZGMCMiIz5GJiNGLEY2I0YyRiojRjlGKCMiI0JGJiNGNEYwI0YwRi4jRjxGKCMiIipGKiMiIzlGKCMiI0hGJkYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L62" 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="PkkjUFBHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIiU7RioiI0o3Ig==">PTYiNiQ7IiIiIiIlO0YmIiNKRVxbbCE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L63" 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="L64" 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],subs(delta=1,u[i-1](t))));od;od:</Text-field>
</Input>
</Group>
<Group labelreference="L65" 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="L66" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">surfdata( plotdata, title=&quot;Figure Exp. 5.33.&quot;,axes=boxed, labels=[x,t,u],orientation=[45,45]);</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, 5660 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L67" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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</Worksheet>