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<Input>
<Text-field style="Text" layout="Normal">Example 6.5 Potential Distribution in a Hull Cell</Text-field>
</Input>
</Group>
<Group labelreference="L76" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart;with(plottools):with(linalg):with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L74" 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)=-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="PkkjZ2VHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkieUdGJC1JIiRHRig2JEYuIiIjLCQtRic2JEYqLUYwNiRGLUYyISIi">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC1JInVHNiI2JEkieEdGK0kieUdGK0YuRi4sJC1GJDYkLUYkNiRGKUYtRi0hIiI=</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Digits:=20;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknRGlnaXRzRzYiIiM/">IiM/</Equation></Text-field>
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</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=diff(u(x,y),x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkieUdGJEYs">LUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHNiI2JEkieEdGKEkieUdGKEYq</Equation></Text-field>
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<Group labelreference="L6" 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>
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<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc3:=u(x,y)-1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMzRzYiLCYtSSJ1R0YkNiRJInhHRiRJInlHRiQiIiJGKyEiIg==">LCYtSSJ1RzYiNiRJInhHRiVJInlHRiUiIiIhIiJGKQ==</Equation></Text-field>
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<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc4:=u(x,y);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmM0RzYiLUkidUdGJDYkSSJ4R0YkSSJ5R0Yk">LUkidUc2IjYkSSJ4R0YkSSJ5R0Yk</Equation></Text-field>
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<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq_cathode:=y=1+0.5*x;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkrZXFfY2F0aG9kZUc2Ii9JInlHRiQsJiIiIkYoKiYkIiImISIiRihJInhHRiRGKEYo">L0kieUc2IiwmIiIiRiZJInhHRiQkIiImISIi</Equation></Text-field>
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<Group labelreference="L10" 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>
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<Group labelreference="L11" 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="L12" 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="L13" 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="L14" 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="L15" 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="PkkkYmMxRzYiLCQqKCMiIiIiIiNGKEkiaEdGJCEiIiwoLSZJInVHRiQ2I0YpNiNJJXpldGFHRiRGKyomIiIkRigtJkYvNiMiIiFGMUYoRisqJiIiJUYoLSZGLzYjRihGMUYoRihGKEYo">LCQqJkkiaEc2IiEiIiwoLSZJInVHRiU2IyIiIzYjSSV6ZXRhR0YlRiYtJkYqNiMiIiFGLSEiJC0mRio2IyIiIkYtIiIlRjcjRjdGLA==</Equation></Text-field>
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</Group>
<Group labelreference="L16" 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>
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<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=10;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTkc2IiIjNQ==">IiM1</Equation></Text-field>
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</Group>
<Group labelreference="L18" 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="PiZJI2VxRzYiNiMiIiEsJCooIyIiIiIiI0YrSSJoR0YlISIiLCgtJkkidUdGJTYjRiw2I0klemV0YUdGJUYuKiYiIiRGKy0mRjJGJkY0RitGLiomIiIlRistJkYyNiNGK0Y0RitGK0YrRis=">LCQqJkkiaEc2IiEiIiwoLSZJInVHRiU2IyIiIzYjSSV6ZXRhR0YlRiYtJkYqNiMiIiFGLSEiJC0mRio2IyIiIkYtIiIlRjcjRjdGLA==</Equation></Text-field>
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<Group labelreference="L19" 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>
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<Group labelreference="L20" 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="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u[0](zeta):=(solve(eq[0],u[0](zeta)));</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi0mSSJ1RzYiNiMiIiE2I0klemV0YUdGJiwmKiYjIiIiIiIkRi4tJkYlNiMiIiNGKUYuISIiKiYjIiIlRi9GLi0mRiU2I0YuRilGLkYu">LCYtJkkidUc2IjYjIiIjNiNJJXpldGFHRiYjISIiIiIkLSZGJTYjIiIiRikjIiIlRi0=</Equation></Text-field>
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<Group labelreference="L22" 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>
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<Group labelreference="L23" 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="L24" 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="L25" 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="L26" 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="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=genmatrix(eqns,Y,'b1'):</Text-field>
</Input>
</Group>
<Group labelreference="L28" 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="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalm(A):</Text-field>
</Input>
</Group>
<Group labelreference="L30" 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="L31" 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>
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<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">J:=jordan(A,S):</Text-field>
</Input>
</Group>
<Group labelreference="L33" 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="L34" 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="L35" 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="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat2:=evalm(mat1&amp;*b2):</Text-field>
</Input>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat2:=map(expand,mat2):</Text-field>
</Input>
</Group>
<Group labelreference="L38" 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="L39" 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>
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<Group labelreference="L40" 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="L41" 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="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalm(Y0):</Text-field>
</Input>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=evalm(mat&amp;*Y0+mat3):</Text-field>
</Input>
</Group>
<Group labelreference="L44" 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="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="PiZJI0VxRzYiNiMiIiIsJiZJInBHRiVGJkYnRichIiI=">LCYmSSJwRzYiNiMiIiJGJyEiIkYn</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiMsJiZJInBHRiVGJiIiIkYrISIi">LCYmSSJwRzYiNiMiIiMiIiIhIiJGKA==</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiQsJiZJInBHRiVGJiIiIkYrISIi">LCYmSSJwRzYiNiMiIiQiIiIhIiJGKA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiUsJiZJInBHRiVGJiIiIkYrISIi">LCYmSSJwRzYiNiMiIiUiIiIhIiJGKA==</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiYsJiZJInBHRiVGJiIiIkYrISIi">LCYmSSJwRzYiNiMiIiYiIiIhIiJGKA==</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIicsJiZJInBHRiVGJiIiIkYrISIi">LCYmSSJwRzYiNiMiIiciIiIhIiJGKA==</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIigsJiZJInBHRiVGJiIiIkYrISIi">LCYmSSJwRzYiNiMiIigiIiIhIiJGKA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiksJiZJInBHRiVGJiIiIkYrISIi">LCYmSSJwRzYiNiMiIikiIiIhIiJGKA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIiosJiZJInBHRiVGJiIiIkYrISIi">LCYmSSJwRzYiNiMiIioiIiIhIiJGKA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI0VxRzYiNiMiIzUsJiZJInBHRiVGJiIiIkYrISIi">LCYmSSJwRzYiNiMiIzUiIiIhIiJGKA==</Equation></Text-field>
</Output>
</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*Y[N+i,1],u(x,y)=Y[i,1],bc4));od:</Text-field>
</Input>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do Eq[N+i]:=evalf(subs(zeta=epsilon/h*(1+0.5*i*h),Eq[N+i]));od:</Text-field>
</Input>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">csol:=solve({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="PkklY3NvbEc2Ijw2LyZJInBHRiQ2IyIiJCQiIiIiIiEvJkYoNiMiIiVGKy8mRig2IyIiJkYrLyZGKDYjIiInRisvJkYoNiMiIihGKy8mRig2IyIiKkYrLyZGKDYjIiIpRisvJkYoNiMiIiNGKy8mRig2I0YsRisvJkYoNiMiIzVGKy8mSSJjR0YkRikkITUxU0pLeC9BYWJ4ISNALyZGU0YwJCE1YkNSd1dNWjYweEZWLyZGU0Y0JCE1M25pSygpKWZUJ1t3RlYvJkZTRjgkITUjKTM7ISpITyZvNGYoRlYvJkZTRjwkITVEWERBQ08hW25gKEZWLyZGU0ZEJCE1KnkqZUE7PCEpNCFcKEZWLyZGU0ZAJCE1XCZlbSticnZWWChGVi8mRlNGTCQhNXBxXUsnUVM8MiN5RlYvJkZTRk8kITVGQy9xOiQpUS9LdUZWLyZGU0ZIJCE1PENrKnB6IjNNJnooRlY=">PDYvJkkicEc2IjYjIiIkJCIiIiIiIS8mRiU2IyIiJUYpLyZGJTYjIiImRikvJkYlNiMiIidGKS8mRiU2IyIiKEYpLyZGJTYjIiIqRikvJkYlNiMiIilGKS8mRiU2IyIiI0YpLyZGJTYjRipGKS8mRiU2IyIjNUYpLyZJImNHRiZGJyQhNTFTSkt4L0FhYnghI0AvJkZRRi4kITViQ1J3V01aNjB4RlQvJkZRRjIkITUzbmlLKCkpZlQnW3dGVC8mRlFGNiQhNSMpMzshKkhPJm80ZihGVC8mRlFGOiQhNURYREFDTyFbbmAoRlQvJkZRRkIkITUqeSplQTs8ISk0IVwoRlQvJkZRRj4kITVcJmVtK2JydlZYKEZULyZGUUZKJCE1cHFdSydRUzwyI3lGVC8mRlFGTSQhNUZDL3E6JClRL0t1RlQvJkZRRkYkITU8Q2sqcHoiM00meihGVA==</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..(1+0.5*i*h),thickness=2);od:</Text-field>
</Input>
</Group>
<Group labelreference="L77" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 0 to N+1 do
  pl[i]:=line([1.2,0.3+i*0.05],[0.9,evalf(subs(y=0.9,u[i](y)))],thickness=1,linestyle=solid);
  pt[i]:=textplot([1.2,0.3+i*0.05,typeset(u[i],&quot;(y)&quot;)],align=right):
end do:</Text-field>
</Input>
</Group>
<Group labelreference="L55" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display([seq(p[i],i=0..N+1,2),seq(pl[i],i=0..N+1,2),seq(pt[i],i=0..N+1,2)],axes=boxed,title=&quot;Fig. Exp. 6.13.&quot;,labels=[y,&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, 31280 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">M:=10;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTUc2IiIjNQ==">IiM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T1:=[seq(evalf(i/M),i=0..M)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVDFHNiI3LSQiIiFGJyQiNSsrKysrKysrKzUhIz8kIjUrKysrKysrKys/RiokIjUrKysrKysrKytJRiokIjUrKysrKysrKytTRiokIjUrKysrKysrKytdRiokIjUrKysrKysrKytnRiokIjUrKysrKysrKytxRiokIjUrKysrKysrKyshKUYqJCI1KysrKysrKysrISpGKiQiIiJGJw==">Ny0kIiIhRiQkIjUrKysrKysrKys1ISM/JCI1KysrKysrKysrP0YnJCI1KysrKysrKysrSUYnJCI1KysrKysrKysrU0YnJCI1KysrKysrKysrXUYnJCI1KysrKysrKysrZ0YnJCI1KysrKysrKysrcUYnJCI1KysrKysrKysrISlGJyQiNSsrKysrKysrKyEqRickIiIiRiQ=</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+1 do P[j]:=plot([seq([h*i,evalf(subs(y=T1[j]*(1+0.5*i*h),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,0))],i=0..N+1)],style=line,thickness=3,axes=boxed):</Text-field>
</Input>
</Group>
<Group labelreference="L78" 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]*(1+0.5*5*h),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;Fig. Exp. 6.14.&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, 23436 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 N+2 do PP[i,1]:=1;PP[i,Ny]:=0;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 Ny-1 do PP[i,j]:=evalf(subs(y=(j-1)*(1+0.5*(i-1)*h)/(Ny-1),u[i-1](y)));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)/(N+1),(j-1)*(1+0.5*(i-1)*h)/(Ny-1),PP[i,j]], i=1..N+2)], j=1..Ny)]:</Text-field>
</Input>
</Group>
<Group labelreference="L66" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">surfdata(plotdata,axes=boxed,title=&quot;Fig. Exp. 6.15.&quot;, labels=[x,y,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, 24496 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L67" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">surfdata(plotdata,axes=boxed,title=&quot;Fig. Exp. 6.15.&quot;,labels=[x,y,u],orientation=[120,0] ,style=patchnogrid);</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, 24616 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L68" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to N do curr[i]:=evalf(subs(y=1+0.5*i*h,diff(u[i](y),y)));od:</Text-field>
</Input>
</Group>
<Group labelreference="L69" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">curr[0]:=4/3*curr[1]-1/3*curr[2];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJWN1cnJHNiI2IyIiISQhNVFpcUkuYWhLazohIz4=">JCE1UWlxSS5haEtrOiEjPg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L70" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">curr[N+1]:=4/3*curr[N]-1/3*curr[N-1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJWN1cnJHNiI2IyIjNiQhNStyTFYiZSUqWylmRCEjPw==">JCE1K3JMViJlJSpbKWZEISM/</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L71" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">avecurr:=sum(curr[k],k=0..N+1)/(N+2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkoYXZlY3Vyckc2IiQhNTszSEw7OXlbUXMhIz8=">JCE1OzNITDs5eVtRcyEjPw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L72" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([seq([i*h,curr[i]/avecurr],i=0..N+1)],thickness=4,axes=boxed,style=point,labels=[x,'i/iavg']);</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">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L73" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>