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<Task>
</Task>
<Group labelreference="L69" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Example 6.4</Text-field>
</Input>
</Group>
<Group labelreference="L70" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart;with(linalg):with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L68" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group>
<Group labelreference="L3" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ge:=diff(u(x,y),y$2)=-epsilon^2*diff(u(x,y),x$2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZ2VHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkieUdGJC1JIiRHRig2JEYuIiIjLCQqJilJKGVwc2lsb25HRiRGMiIiIi1GJzYkRiotRjA2JEYtRjJGNyEiIg==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC1JInVHNiI2JEkieEdGK0kieUdGK0YuRi4sJComSShlcHNpbG9uR0YrIiIjLUYkNiQtRiQ2JEYpRi1GLSIiIiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=u(x,y)-0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLUkidUdGJDYkSSJ4R0YkSSJ5R0Yk">LUkidUc2IjYkSSJ4R0YkSSJ5R0Yk</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=diff(u(x,y),x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkieUdGJEYs">LUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHNiI2JEkieEdGKEkieUdGKEYq</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L74" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The nonlinear boundary condition at y = 0 is entered:</Text-field>
</Input>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc3:=diff(u(x,y),y)-u(x,y)^4;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMzRzYiLCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkidUdGJDYkSSJ4R0YkSSJ5R0YkRi4iIiIqJClGKiIiJUYvISIi">LCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkidUc2IjYkSSJ4R0YpSSJ5R0YpRiwiIiIqJEYnIiIlISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc4:=u(x,y)-1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmM0RzYiLCYtSSJ1R0YkNiRJInhHRiRJInlHRiQiIiJGKyEiIg==">LCYtSSJ1RzYiNiRJInhHRiVJInlHRiUiIiIhIiJGKQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">H:=0.5;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiSEc2IiQiIiYhIiI=">JCIiJiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">epsilon:=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkoZXBzaWxvbkc2IiIiIg==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxf:=1/2/h*(-u[m+2](zeta)-3*u[m](zeta)+4*u[m+1](zeta)):</Text-field>
</Input>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydxb:=1/2/h*(u[m-2](zeta)+3*u[m](zeta)-4*u[m-1](zeta)):</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydx:=1/2/h*(u[m+1](zeta)-u[m-1](zeta)):</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">d2ydx2:=1/h^2*(u[m-1](zeta)-2*u[m](zeta)+u[m+1](zeta)):</Text-field>
</Input>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=subs(diff(u(x,y),x)=subs(m=0,dydxf),u(x,y)=u[0](zeta),bc1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLSZJInVHRiQ2IyIiITYjSSV6ZXRhR0Yk">LSZJInVHNiI2IyIiITYjSSV6ZXRhR0Yl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=subs(diff(u(x,y),x)=subs(m=N+1,dydxb),u(x,y)=u[N+1](zeta),bc2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLCQqKCMiIiIiIiNGKEkiaEdGJCEiIiwoLSZJInVHRiQ2IywmSSJOR0YkRihGKEYrNiNJJXpldGFHRiRGKComIiIkRigtJkYvNiMsJkYyRihGKEYoRjNGKEYoKiYiIiVGKC0mRi82I0YyRjNGKEYrRihGKA==">LCQqJkkiaEc2IiEiIiwoLSZJInVHRiU2IywmSSJOR0YlIiIiRiZGLjYjSSV6ZXRhR0YlRi4tJkYqNiMsJkYtRi5GLkYuRi8iIiQtJkYqNiNGLUYvISIlRi4jRi4iIiM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=10;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTkc2IiIjNQ==">IiM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="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="PiZJI2VxRzYiNiMiIiEtJkkidUdGJUYmNiNJJXpldGFHRiU=">LSZJInVHNiI2IyIiITYjSSV6ZXRhR0Yl</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="PiZJI2VxRzYiNiMiIzYsJCooIyIiIiIiI0YrSSJoR0YlISIiLCgtJkkidUdGJTYjIiIqNiNJJXpldGFHRiVGKyomIiIkRistJkYyRiZGNUYrRisqJiIiJUYrLSZGMjYjIiM1RjVGK0YuRitGKw==">LCQqJkkiaEc2IiEiIiwoLSZJInVHRiU2IyIiKjYjSSV6ZXRhR0YlIiIiLSZGKjYjIiM2Ri0iIiQtJkYqNiMiIzVGLSEiJUYvI0YvIiIj</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[N+1+i]:=diff(u[N+1+i](zeta),zeta)= subs(diff(u(x,y),x$2) = subs(m=i,d2ydx2),diff(u(x,y),x) = subs(m=i,dydx),diff(u(x,y),y)=epsilon/h*u[N+1+i](zeta),u(x,y)=u[i](zeta),x=i*h,rhs(h^2/epsilon^2*ge));od:</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u[0](zeta):=(solve(eq[0],u[0](zeta)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiE2I0klemV0YUdGJkYo">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u[N+1](zeta):=solve(eq[N+1],u[N+1](zeta));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIzY2I0klemV0YUdGJiwmKiYjIiIiIiIkRi4tJkYlNiMiIipGKUYuISIiKiYjIiIlRi9GLi0mRiU2IyIjNUYpRi5GLg==">LCYtJkkidUc2IjYjIiIqNiNJJXpldGFHRiYjISIiIiIkLSZGJTYjIiM1RikjIiIlRi0=</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]:=diff(u[i](zeta),zeta)= u[N+1+i](zeta);od:</Text-field>
</Input>
</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:for i from 1 to N do eq[N+1+i]:=eval(eq[N+1+i]);od:</Text-field>
</Input>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqns:=[seq(rhs(eq[j]),j=1..N),seq(rhs(eq[N+1+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](zeta),i=1..N),seq(u[N+1+i](zeta),i=1..N)]:</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=genmatrix(eqns,Y,'b1'):</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">if N&gt;2 then A:=map(evalf,A):end:</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalm(A):</Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b:=matrix(2*N,1):for i from 1 to 2*N do b[i,1]:=-b1[i];od:evalm(b):</Text-field>
</Input>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">h:=eval(1/(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="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">J:=jordan(A,S):</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=evalm(S&amp;*exponential(J,zeta)&amp;*inverse(S)):</Text-field>
</Input>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat1:=evalm(subs(zeta=zeta-zeta1,evalm(mat))):</Text-field>
</Input>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b2:=evalm(subs(zeta=zeta1,evalm(b))):</Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat2:=evalm(mat1&amp;*b2):</Text-field>
</Input>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat2:=map(expand,mat2):</Text-field>
</Input>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat3:=map(int,mat2,zeta1=0..zeta):</Text-field>
</Input>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y0:=matrix(2*N,1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjWTBHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIz87RipGKjci">PTYiNiQ7IiIiIiM/O0YmRiZFXFtsIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do Y0[i,1]:=p[i];od:</Text-field>
</Input>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do Y0[N+i,1]:=c[i]:od:</Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalm(Y0):</Text-field>
</Input>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=evalm(mat&amp;*Y0+mat3):</Text-field>
</Input>
</Group>
<Group labelreference="L76" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">For calculating the constants the solution is evaluated at y = 0 and y = H:</Text-field>
</Input>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol0:=map(eval,evalm(subs(zeta=0,evalm(Y)))):</Text-field>
</Input>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol1:=map(eval,evalm(subs(zeta=epsilon*H/h,evalm(Y)))):</Text-field>
</Input>
</Group>
<Group labelreference="L77" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The boundary condition at y = 0 (bc3) yields N nonlinear algebraic equations:</Text-field>
</Input>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do Eq[i]:=subs(diff(u(x,y),y)=epsilon/h*c[i],u(x,y)=p[i],x=i*h,bc3);od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiIsJiomIiM2RicmSSJjR0YlRiZGJ0YnKiQpJkkicEdGJUYmIiIlRichIiI=">LCYmSSJjRzYiNiMiIiIiIzYqJCZJInBHRiVGJiIiJSEiIg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiMsJiomIiM2IiIiJkkiY0dGJUYmRitGKyokKSZJInBHRiVGJiIiJUYrISIi">LCYmSSJjRzYiNiMiIiMiIzYqJCZJInBHRiVGJiIiJSEiIg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiQsJiomIiM2IiIiJkkiY0dGJUYmRitGKyokKSZJInBHRiVGJiIiJUYrISIi">LCYmSSJjRzYiNiMiIiQiIzYqJCZJInBHRiVGJiIiJSEiIg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiUsJiomIiM2IiIiJkkiY0dGJUYmRitGKyokKSZJInBHRiVGJkYnRishIiI=">LCYmSSJjRzYiNiMiIiUiIzYqJCZJInBHRiVGJkYnISIi</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiYsJiomIiM2IiIiJkkiY0dGJUYmRitGKyokKSZJInBHRiVGJiIiJUYrISIi">LCYmSSJjRzYiNiMiIiYiIzYqJCZJInBHRiVGJiIiJSEiIg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIicsJiomIiM2IiIiJkkiY0dGJUYmRitGKyokKSZJInBHRiVGJiIiJUYrISIi">LCYmSSJjRzYiNiMiIiciIzYqJCZJInBHRiVGJiIiJSEiIg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIigsJiomIiM2IiIiJkkiY0dGJUYmRitGKyokKSZJInBHRiVGJiIiJUYrISIi">LCYmSSJjRzYiNiMiIigiIzYqJCZJInBHRiVGJiIiJSEiIg==</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiksJiomIiM2IiIiJkkiY0dGJUYmRitGKyokKSZJInBHRiVGJiIiJUYrISIi">LCYmSSJjRzYiNiMiIikiIzYqJCZJInBHRiVGJiIiJSEiIg==</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiosJiomIiM2IiIiJkkiY0dGJUYmRitGKyokKSZJInBHRiVGJiIiJUYrISIi">LCYmSSJjRzYiNiMiIioiIzYqJCZJInBHRiVGJiIiJSEiIg==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzUsJiomIiM2IiIiJkkiY0dGJUYmRitGKyokKSZJInBHRiVGJiIiJUYrISIi">LCYmSSJjRzYiNiMiIzUiIzYqJCZJInBHRiVGJiIiJSEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L75" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The boundary condition at y = H yields N linear algebraic equations:</Text-field>
</Input>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do Eq[N+i]:=evalf(subs(diff(u(x,y),y)=epsilon/h*sol1[N+i,1],u(x,y)=sol1[i,1],bc4));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LEwmSSJwRzYiNiMiIiIkIituL15lUSEiJyZGJDYjIiIjJCErOWVCYFlGKiZGJDYjIiIkJCIrZ1hGTElGKiZGJDYjIiIlJCErPCU9cUciRiomRiQ2IyIiJiQiK3RmIkgjUSEiKCZGJDYjIiInJCErUXBHKFEpISIpJkYkNiMiIigkIitRWHM9OEZFJkYkNiMiIikkISo+cixgI0ZFJkYkNiMiIiokIip0O2NTKSEiKiZGJDYjIiM1JCEqckQleUBGRSZJImNHRiVGJiQiK21lQCI+I0YqJkZmbkYsJCErYHlWJFwjRiomRmZuRjEkIitqJFEjKVwiRiomRmZuRjYkISs1O3lfZEY/JkZmbkY7JCIrVVduWzpGPyZGZm5GQSQhKyN6QSJbSkZFJkZmbkZHJCIqW2tRaCNGRSZGZm5GTCQhKj8uLk8kRkUmRmZuRlEkISsjPUkiZUJGVSZGZm5GVyQhKidIKno0J0ZFJCEiIiIiIUYn</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LEwmSSJwRzYiNiMiIiIkISt5dXhfWSEiJyZGJDYjIiIjJCIrPXZmIypvRiomRiQ2IyIiJCQhK3RYaVJmRiomRiQ2IyIiJSQiK1c8KWVUJEYqJkYkNiMiIiYkISsmKjM6cThGKiZGJDYjIiInJCIrZltGcVIhIigmRiQ2IyIiKCQhK1RJbiZSKSEiKSZGJDYjIiIpJCIrZnkrLTpGSiZGJDYjIiIqJCErPz9GTUchIiomRiQ2IyIjNSQiKik0IyllTEZKJkkiY0dGJUYmJCErREVEJVwjRiomRmZuRiwkIitzMl0obyRGKiZGZm5GMSQhK2tNQXJJRiomRmZuRjYkIisrTSo+bCJGKiZGZm5GOyQhK187N1dnRkQmRmZuRkAkIitLdEpTO0ZEJkZmbkZGJCEraENHS0NGSiZGZm5GTCQiK15nNXY3RkomRmZuRlEkIisoUjxxSShGVSZGZm5GVyQiK0tMIjRoIkZKJCEiIiIiIUYn</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LEwmSSJwRzYiNiMiIiIkIitDJ1JMLiQhIicmRiQ2IyIiIyQhKylSZS8lZkYqJkYkNiMiIiQkIitaR0V1c0YqJkYkNiMiIiUkIStYa0lCZ0YqJkYkNiMiIiYkIis5dVpITUYqJkYkNiMiIickISt4dy90OEYqJkYkNiMiIigkIitqPFVfUiEiKCZGJDYjIiIpJCErZVJPPycpISIpJkYkNiMiIiokIitxcUwtOkZPJkYkNiMiIzUkISs4QT0uVyEiKiZJImNHRiVGJiQiK1Q8biZcIkYqJkZmbkYsJCErJTM7RTIkRiomRmZuRjEkIis9XiMqUlFGKiZGZm5GNiQhK3pbXzBKRiomRmZuRjskIisjPiE0XDtGKiZGZm5GQCQhK0gjcFk8J0ZJJkZmbkZFJCIraEQ5bzlGSSZGZm5GSyQhK2lLJ0hjJUZPJkZmbkZRJCErZ3QuXjVGTyZGZm5GViQhKzJBIlInR0ZPJCEiIiIiIUYn</Equation></Text-field>
</Output>
<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>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzosTComJCIrVG9ZQlEhIigiIiImSSJwR0YlNiNGLUYtRi0qJiQiK2x2V3E4ISInRi0mRi82IyIiI0YtISIiKiYkIitLJUcmSE1GNEYtJkYvNiMiIiRGLUYtKiYkIishUnhdLSdGNEYtJkYvNiMiIiVGLUY4KiYkIissVlYpRyhGNEYtJkYvNiMiIiZGLUYtKiYkIitDJCpbRGdGNEYtJkYvNiMiIidGLUY4KiYkIit6YD5ITUY0Ri0mRi82IyIiKEYtRi0qJiQiK1xhKD1QIkY0Ri0mRi82IyIiKUYtRjgqJiQiKyRwTHUhUkYsRi0mRi82IyIiKkYtRi0qJiQiK3EpNCcqeichIilGLSZGLzYjIiM1Ri1GOComJCIrdXJMMzpGLEYtJkkiY0dGJUYwRi1GLSomJCIrTC8vVmhGLEYtJkZob0Y2Ri1GOComJCIrPUIpW2siRjRGLSZGaG9GPUYtRi0qJiQiKy1fODxKRjRGLSZGaG9GQ0YtRjgqJiQiKzYpZnIjUUY0Ri0mRmhvRklGLUYtKiYkIisrKmVrNyRGNEYtJkZob0ZPRi1GOComJCIrKGVvcWkiRjRGLSZGaG9GVUYtRi0qJiQiK19tXS9rRixGLSZGaG9GZW5GLUY4KiYkIitDWmkuN0YsRi0mRmhvRltvRi1GLSomJCIrXD9eJ3opRmBvRi0mRmhvRmJvRi1GOCRGLSIiIUY4">LEwmSSJwRzYiNiMiIiIkIitUb1lCUSEiKCZGJDYjIiIjJCErbHZXcTghIicmRiQ2IyIiJCQiK0slRyZITUYwJkYkNiMiIiUkISshUnhdLSdGMCZGJDYjIiImJCIrLFZWKUcoRjAmRiQ2IyIiJyQhK0MkKltEZ0YwJkYkNiMiIigkIit6YD5ITUYwJkYkNiMiIikkIStcYSg9UCJGMCZGJDYjIiIqJCIrJHBMdSFSRiomRiQ2IyIjNSQhK3EpNCcqeichIikmSSJjR0YlRiYkIit1ckwzOkYqJkZlbkYsJCErTC8vVmhGKiZGZW5GMiQiKz1CKVtrIkYwJkZlbkY3JCErLV84PEpGMCZGZW5GPCQiKzYpZnIjUUYwJkZlbkZBJCErKyplazckRjAmRmVuRkYkIisoZW9xaSJGMCZGZW5GSyQhK19tXS9rRiomRmVuRlAkIitDWmkuN0YqJkZlbkZVJCErXD9eJ3opRlkkISIiIiIhRic=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LEwmSSJwRzYiNiMiIiIkIStTX1dGJCkhIikmRiQ2IyIiIyQiKzZAKj0nUiEiKCZGJDYjIiIkJCErJCozLnM4ISInJkYkNiMiIiUkIis3SyUpSE1GNiZGJDYjIiImJCErLG8uRGdGNiZGJDYjIiInJCIrJ0g5JylHKEY2JkYkNiMiIigkISsuMC1DZ0Y2JkYkNiMiIikkIitkYyFSVSRGNiZGJDYjIiIqJCErT3A3SzhGNiZGJDYjIiM1JCIrelcpPipHRjAmSSJjR0YlRiYkISslRyZmVkRGKiZGZW5GLCQiK21FITNwIkYwJkZlbkYyJCErVWlpRGZGMCZGZW5GOCQiK0VwOHc7RjYmRmVuRj0kISstM1N3SUY2JkZlbkZCJCIrKG88eihRRjYmRmVuRkckISsieThhMSRGNiZGZW5GTCQiK004XCZwIkY2JkZlbkZRJCErdnJJb2FGMCZGZW5GViQiKz80M3Y+RjAkISIiIiIhRic=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LEwmSSJwRzYiNiMiIiIkIitfUiFwUCIhIikmRiQ2IyIiIyQhKzxkNDEmKUYqJkYkNiMiIiQkIisjeTtJJ1IhIigmRiQ2IyIiJSQhK3ArNHM4ISInJkYkNiMiIiYkIispR10oSE1GOyZGJDYjIiInJCErMyJ6Vi0nRjsmRiQ2IyIiKCQiK3V1PCNHKEY7JkYkNiMiIikkIStJRCNcKWZGOyZGJDYjIiIqJCIrUWwzRUtGOyZGJDYjIiM1JCErbGtuKnopRjUmSSJjR0YlRiYkISlpTENvRiomRmVuRiwkISsnbyRwUVRGKiZGZW5GMSQiK3gueU45RjUmRmVuRjckISsyPk4lRydGNSZGZW5GPSQiK2cwa0g7RjsmRmVuRkIkISs3O1tMSkY7JkZlbkZHJCIrXXV6MlFGOyZGZW5GTCQhK0VRNUlKRjsmRmVuRlEkIitlPjJIOkY7JkZlbkZWJCErKVssTyhbRjUkISIiIiIhRic=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LEwmSSJwRzYiNiMiIiIkISooR1UheSIhIikmRiQ2IyIiIyQiK1BeUiVSIkYqJkYkNiMiIiQkIStbXSZbXSlGKiZGJDYjIiIlJCIrW0RXaVIhIigmRiQ2IyIiJiQhK0UlUjhQIiEiJyZGJDYjIiInJCIrJVtqT1UkRkAmRiQ2IyIiKCQhKzB0dyUpZkZAJkYkNiMiIikkIithJVxaMyhGQCZGJDYjIiIqJCErQHk8Ul9GQCZGJDYjIiM1JCIrJypIRGw8RkAmSSJjR0YlRiYkIipCMTQpUUYqJkZlbkYsJCIrLGd0VDhGKiZGZW5GMSQhK1RaSXM8RiomRmVuRjYkIis0Jio9cDxGOiZGZW5GPCQhK2J2Vl1lRjomRmVuRkIkIislUT4ybyJGQCZGZW5GRyQhK10oKVxjSUZAJkZlbkZMJCIreVFALlFGQCZGZW5GUSQhK1RkbEVGRkAmRmVuRlYkIitNNC0meSpGOiQhIiIiIiFGJw==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LEwmSSJwRzYiNiMiIiIkIipaNTAmPSEiKiZGJDYjIiIjJCErKD5ATXkiRiomRiQ2IyIiJCQiK3hhXidRIiEiKSZGJDYjIiIlJCErYG9VSSUpRjUmRiQ2IyIiJiQiK0hHTyxSISIoJkYkNiMiIickISsmW2k9TCIhIicmRiQ2IyIiKCQiKzpIL0VLRkYmRiQ2IyIiKSQhK2h0R1JfRkYmRiQ2IyIiKiQiKzxCI1wuJkZGJkYkNiMiIzUkISs8MWoyP0ZGJkkiY0dGJUYmJCErXkFCInAjRiomRmZuRiwkISspR0VKLCdGKiZGZm5GMSQhK2lIPk1PRiomRmZuRjckIStrYTJxVEY1JkZmbkY8JCIrVzhOTjlGQCZGZm5GQiQhK3MoXGs0J0ZAJkZmbkZIJCIrKG9pdmIiRkYmRmZuRk0kIStaalspeSNGRiZGZm5GUiQiK1hIbHVGRkYmRmZuRlckIStxQUQjPSJGRiQhIiIiIiFGJw==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LEwmSSJwRzYiNiMiIiIkISdnOygqISIpJkYkNiMiIiMkIikqKUciNCJGKiZGJDYjIiIkJCErUjBYTDUhIiomRiQ2IyIiJSQiKzNiNmR4RjUmRiQ2IyIiJiQhKyIqKnlFWyVGKiZGJDYjIiInJCIrOSpSYyM+ISIoJkYkNiMiIigkIStYekBqZUZFJkYkNiMiIikkIitgc1B3NiEiJyZGJDYjIiIqJCErJ1IpKnpMIkZQJkYkNiMiIzUkIiskRyRmWGZGRSZJImNHRiVGJiQiKTssYWRGKiZGZm5GLCQiKic9J1s9IkYqJkZmbkYxJCIrU1ZDPDlGNSZGZm5GNyQiKyhcbGoiXEY1JkZmbkY8JCEranohNFEiRiomRmZuRkEkIitDTiJRTSlGKiZGZm5GRyQhK09GcCFvI0ZFJkZmbkZMJCIrJSlIQ0loRkUmRmZuRlIkIStpVVBldkZFJkZmbkZXJCIrJkdCQXQkRkUkISIiIiIhRic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">csol:=fsolve({seq(Eq[i],i=1..2*N)},{seq(c[i],i=1..N),seq(p[i],i=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="L48" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">csol:=fsolve({seq(Eq[i],i=1..2*N)},{seq(c[i]=0..1,i=1..N),seq(p[i]=0..1,i=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="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">assign(csol);</Text-field>
</Input>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">YY:=map(eval,Y):</Text-field>
</Input>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N do u[i](zeta):=eval((YY[i,1]));od:</Text-field>
</Input>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 do u[i](zeta):=eval(u[i](zeta));od:</Text-field>
</Input>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 do u[i](y):=eval(subs(zeta=epsilon*y/h,u[i](zeta)));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 p[i]:=plot(u[i](y),y=0..H,thickness=3);od:</Text-field>
</Input>
</Group>
<Group labelreference="L72" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pp:=plot([seq(u[i](y),i=0..N+1,2)],y=0..H,thickness=3,legend=[seq(typeset(u[i],&quot;(y)&quot;),i=0..N+1,2)]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="[encoded data, 8596 characters]">[encoded data, 8564 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L55" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({pp},axes=boxed,title=&quot;Figure Exp. 6.10.&quot;,labels=[y,&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="true">[encoded data, 30224 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">M:=5;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTUc2IiIiJg==">IiIm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T1:=[seq(evalf(i*H/M),i=0..M)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVDFHNiI3KCQiIiFGJyQiKysrKys1ISM1JCIrKysrKz9GKiQiKysrKytJRiokIisrKysrU0YqJCIrKysrK11GKg==">NygkIiIhRiQkIisrKysrNSEjNSQiKysrKys/RickIisrKysrSUYnJCIrKysrK1NGJyQiKysrKytdRic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L58" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for j from 1 to M do P[j]:=plot([seq([h*i,evalf(subs(y=T1[j],evalf(u[i](y))))],i=0..N+1)],style=line,thickness=3,axes=boxed,view=[0..1,0..1.1]):od:</Text-field>
</Input>
</Group>
<Group labelreference="L59" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P[M+1]:=plot([seq([h*i,evalf(subs(x=i*h,1))],i=0..N+1)],style=line,thickness=3,axes=boxed):</Text-field>
</Input>
</Group>
<Group labelreference="L73" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for j from 1 to M+1 do
  pt[j]:=textplot([0.5,evalf(subs(y=T1[j],u[5](y))),typeset(y,sprintf(&quot;=%4.2f&quot;,T1[j]))],align={above});
od:</Text-field>
</Input>
</Group>
<Group labelreference="L60" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({seq(P[i],i=1..M+1),seq(pt[i],i=1..M+1)},title=&quot;Figure Exp.6.11.&quot;,labels=[x,u]);</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, 13240 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L61" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ny:=30;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjTnlHNiIiI0k=">IiNJ</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L62" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">PP:=matrix(N+2,Ny);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjUFBHNiItSSZhcnJheUclKnByb3RlY3RlZEc2JTsiIiIiIzc7RioiI0k3Ig==">PTYiNiQ7IiIiIiM3O0YmIiNJRVxbbCE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L63" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to Ny do PP[1,i]:=0;od:</Text-field>
</Input>
</Group>
<Group labelreference="L64" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N+2 do PP[i,Ny]:=1;od:</Text-field>
</Input>
</Group>
<Group labelreference="L65" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 2 to N+2 do for j from 1 to Ny-1 do PP[i,j]:=evalf(subs(y=(j-1)*H/(Ny-1),u[i-1](y)));od;od:</Text-field>
</Input>
</Group>
<Group labelreference="L66" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plotdata := [seq([ seq([(i-1)/(N+1),(j-1)*H/(Ny-1),PP[i,j]], i=1..N+2)], j=1..Ny)]:</Text-field>
</Input>
</Group>
<Group labelreference="L67" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">surfdata(plotdata,axes=boxed,title=&quot;Figure Exp. 6.12.&quot;,labels=[x,y,u],orientation=[-120,60] );</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, 17412 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L71" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group>
</Worksheet>