Example 6.1 Rev 1.mw

Example 6.1 

> `*`(r, `*`(estart)); 1; with(plottools); -1; with(linalg); -1; with(plots); -1
 

`*`(r, `*`(estart)) (1)
 

> ge:=diff(u(x,y),y$2)=-epsilon^2*diff(u(x,y),x$2);
 

diff(diff(u(x, y), y), y) = `+`(`-`(`*`(`^`(epsilon, 2), `*`(diff(diff(u(x, y), x), x))))) (2)
 

> bc1:=u(x,y)-0;
 

u(x, y) (3)
 

> bc2:=u(x,y)-0;
 

u(x, y) (4)
 

> bc3:=u(x,y)-0;
 

u(x, y) (5)
 

> bc4:=u(x,y)-1;
 

`+`(u(x, y), `-`(1)) (6)
 

> epsilon:=1;
 

1 (7)
 

> dydxf:=1/2/h*(-u[m+2](zeta)-3*u[m](zeta)+4*u[m+1](zeta));
 

`+`(`/`(`*`(`/`(1, 2), `*`(`+`(`-`(u[`+`(m, 2)](zeta)), `-`(`*`(3, `*`(u[m](zeta)))), `*`(4, `*`(u[`+`(m, 1)](zeta)))))), `*`(h))) (8)
 

> dydxb:=1/2/h*(u[m-2](zeta)+3*u[m](zeta)-4*u[m-1](zeta));
 

`+`(`/`(`*`(`/`(1, 2), `*`(`+`(u[`+`(m, `-`(2))](zeta), `*`(3, `*`(u[m](zeta))), `-`(`*`(4, `*`(u[`+`(m, `-`(1))](zeta))))))), `*`(h))) (9)
 

> dydx:=1/2/h*(u[m+1](zeta)-u[m-1](zeta));
 

`+`(`/`(`*`(`/`(1, 2), `*`(`+`(u[`+`(m, 1)](zeta), `-`(u[`+`(m, `-`(1))](zeta))))), `*`(h))) (10)
 

> d2ydx2:=1/h^2*(u[m-1](zeta)-2*u[m](zeta)+u[m+1](zeta));
 

`/`(`*`(`+`(u[`+`(m, `-`(1))](zeta), `-`(`*`(2, `*`(u[m](zeta)))), u[`+`(m, 1)](zeta))), `*`(`^`(h, 2))) (11)
 

> bc1:=subs(diff(u(x,y),x)=subs(m=0,dydxf),u(x,y)=u[0](zeta),x=0,bc1);
 

u[0](zeta) (12)
 

> bc2:=subs(diff(u(x,y),x)=subs(m=N+1,dydxb),u(x,y)=u[N+1](zeta),x=1,bc2);
 

u[`+`(N, 1)](zeta) (13)
 

> N:=10;
 

10 (14)
 

> eq[0]:=bc1;
 

u[0](zeta) (15)
 

> eq[N+1]:=bc2;
 

u[11](zeta) (16)
 

> 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),u(x,y)=u[i](zeta),x=i*h,rhs(h^2/epsilon^2*ge));od;
 

 

 

 

 

 

 

 

 

 

diff(u[12](zeta), zeta) = `+`(`-`(u[0](zeta)), `*`(2, `*`(u[1](zeta))), `-`(u[2](zeta)))
diff(u[13](zeta), zeta) = `+`(`-`(u[1](zeta)), `*`(2, `*`(u[2](zeta))), `-`(u[3](zeta)))
diff(u[14](zeta), zeta) = `+`(`-`(u[2](zeta)), `*`(2, `*`(u[3](zeta))), `-`(u[4](zeta)))
diff(u[15](zeta), zeta) = `+`(`-`(u[3](zeta)), `*`(2, `*`(u[4](zeta))), `-`(u[5](zeta)))
diff(u[16](zeta), zeta) = `+`(`-`(u[4](zeta)), `*`(2, `*`(u[5](zeta))), `-`(u[6](zeta)))
diff(u[17](zeta), zeta) = `+`(`-`(u[5](zeta)), `*`(2, `*`(u[6](zeta))), `-`(u[7](zeta)))
diff(u[18](zeta), zeta) = `+`(`-`(u[6](zeta)), `*`(2, `*`(u[7](zeta))), `-`(u[8](zeta)))
diff(u[19](zeta), zeta) = `+`(`-`(u[7](zeta)), `*`(2, `*`(u[8](zeta))), `-`(u[9](zeta)))
diff(u[20](zeta), zeta) = `+`(`-`(u[8](zeta)), `*`(2, `*`(u[9](zeta))), `-`(u[10](zeta)))
diff(u[21](zeta), zeta) = `+`(`-`(u[9](zeta)), `*`(2, `*`(u[10](zeta))), `-`(u[11](zeta))) (17)
 

> u[0](zeta):=(solve(eq[0],u[0](zeta)));
 

0 (18)
 

> u[N+1](zeta):=solve(eq[N+1],u[N+1](zeta));
 

0 (19)
 

> for i from 1 to N do eq[i]:=diff(u[i](zeta),zeta)=u[N+1+i](zeta);od;
 

 

 

 

 

 

 

 

 

 

diff(u[1](zeta), zeta) = u[12](zeta)
diff(u[2](zeta), zeta) = u[13](zeta)
diff(u[3](zeta), zeta) = u[14](zeta)
diff(u[4](zeta), zeta) = u[15](zeta)
diff(u[5](zeta), zeta) = u[16](zeta)
diff(u[6](zeta), zeta) = u[17](zeta)
diff(u[7](zeta), zeta) = u[18](zeta)
diff(u[8](zeta), zeta) = u[19](zeta)
diff(u[9](zeta), zeta) = u[20](zeta)
diff(u[10](zeta), zeta) = u[21](zeta) (20)
 

> 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;
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

diff(u[1](zeta), zeta) = u[12](zeta)
diff(u[2](zeta), zeta) = u[13](zeta)
diff(u[3](zeta), zeta) = u[14](zeta)
diff(u[4](zeta), zeta) = u[15](zeta)
diff(u[5](zeta), zeta) = u[16](zeta)
diff(u[6](zeta), zeta) = u[17](zeta)
diff(u[7](zeta), zeta) = u[18](zeta)
diff(u[8](zeta), zeta) = u[19](zeta)
diff(u[9](zeta), zeta) = u[20](zeta)
diff(u[10](zeta), zeta) = u[21](zeta)
diff(u[12](zeta), zeta) = `+`(`*`(2, `*`(u[1](zeta))), `-`(u[2](zeta)))
diff(u[13](zeta), zeta) = `+`(`-`(u[1](zeta)), `*`(2, `*`(u[2](zeta))), `-`(u[3](zeta)))
diff(u[14](zeta), zeta) = `+`(`-`(u[2](zeta)), `*`(2, `*`(u[3](zeta))), `-`(u[4](zeta)))
diff(u[15](zeta), zeta) = `+`(`-`(u[3](zeta)), `*`(2, `*`(u[4](zeta))), `-`(u[5](zeta)))
diff(u[16](zeta), zeta) = `+`(`-`(u[4](zeta)), `*`(2, `*`(u[5](zeta))), `-`(u[6](zeta)))
diff(u[17](zeta), zeta) = `+`(`-`(u[5](zeta)), `*`(2, `*`(u[6](zeta))), `-`(u[7](zeta)))
diff(u[18](zeta), zeta) = `+`(`-`(u[6](zeta)), `*`(2, `*`(u[7](zeta))), `-`(u[8](zeta)))
diff(u[19](zeta), zeta) = `+`(`-`(u[7](zeta)), `*`(2, `*`(u[8](zeta))), `-`(u[9](zeta)))
diff(u[20](zeta), zeta) = `+`(`-`(u[8](zeta)), `*`(2, `*`(u[9](zeta))), `-`(u[10](zeta)))
diff(u[21](zeta), zeta) = `+`(`-`(u[9](zeta)), `*`(2, `*`(u[10](zeta)))) (21)
 

> eqns:=[seq(rhs(eq[j]),j=1..N),seq(rhs(eq[N+1+j]),j=1..N)];
 

[u[12](zeta), u[13](zeta), u[14](zeta), u[15](zeta), u[16](zeta), u[17](zeta), u[18](zeta), u[19](zeta), u[20](zeta), u[21](zeta), `+`(`*`(2, `*`(u[1](zeta))), `-`(u[2](zeta))), `+`(`-`(u[1](zeta)), `...
[u[12](zeta), u[13](zeta), u[14](zeta), u[15](zeta), u[16](zeta), u[17](zeta), u[18](zeta), u[19](zeta), u[20](zeta), u[21](zeta), `+`(`*`(2, `*`(u[1](zeta))), `-`(u[2](zeta))), `+`(`-`(u[1](zeta)), `...
[u[12](zeta), u[13](zeta), u[14](zeta), u[15](zeta), u[16](zeta), u[17](zeta), u[18](zeta), u[19](zeta), u[20](zeta), u[21](zeta), `+`(`*`(2, `*`(u[1](zeta))), `-`(u[2](zeta))), `+`(`-`(u[1](zeta)), `...
[u[12](zeta), u[13](zeta), u[14](zeta), u[15](zeta), u[16](zeta), u[17](zeta), u[18](zeta), u[19](zeta), u[20](zeta), u[21](zeta), `+`(`*`(2, `*`(u[1](zeta))), `-`(u[2](zeta))), `+`(`-`(u[1](zeta)), `...
(22)
 

> Y:=[seq(u[i](zeta),i=1..N),seq(u[N+1+i](zeta),i=1..N)];
 

[u[1](zeta), u[2](zeta), u[3](zeta), u[4](zeta), u[5](zeta), u[6](zeta), u[7](zeta), u[8](zeta), u[9](zeta), u[10](zeta), u[12](zeta), u[13](zeta), u[14](zeta), u[15](zeta), u[16](zeta), u[17](zeta), ...
[u[1](zeta), u[2](zeta), u[3](zeta), u[4](zeta), u[5](zeta), u[6](zeta), u[7](zeta), u[8](zeta), u[9](zeta), u[10](zeta), u[12](zeta), u[13](zeta), u[14](zeta), u[15](zeta), u[16](zeta), u[17](zeta), ...
(23)
 

> A:=genmatrix(eqns,Y,'b1');
 

array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = -1, ( 19, 4 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) ... (24)
 

> if N>2 then A:=map(evalf,A):end;
 

array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0., ( 6, 12 ) = 0., ( 7, 18 ) = 0., ( 18, 7 ) = -1., ( 19, 4 ) = 0., ( 1, 4 ) = 0., ( 2, 4 ) = 0., ( 12, 6 ) = 0., ( 10, 14 ) = 0., ( 5, 20 ) = 0., ( 9, 14 ) = 0.,... (25)
 

> evalm(A);
 

array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0., ( 6, 12 ) = 0., ( 7, 18 ) = 0., ( 18, 7 ) = -1., ( 19, 4 ) = 0., ( 1, 4 ) = 0., ( 2, 4 ) = 0., ( 12, 6 ) = 0., ( 10, 14 ) = 0., ( 5, 20 ) = 0., ( 9, 14 ) = 0.,... (26)
 

> b:=matrix(2*N,1):for i from 1 to 2*N do b[i,1]:=-b1[i];od:evalm(b);
 

array( 1 .. 20, 1 .. 1, [( 10, 1 ) = 0, ( 5, 1 ) = 0, ( 14, 1 ) = 0, ( 12, 1 ) = 0, ( 15, 1 ) = 0, ( 18, 1 ) = 0, ( 9, 1 ) = 0, ( 6, 1 ) = 0, ( 2, 1 ) = 0, ( 7, 1 ) = 0, ( 1, 1 ) = 0, ( 8, 1 ) = 0, ( ... (27)
 

> h:=eval(1/(N+1));
 

`/`(1, 11) (28)
 

> J:=jordan(A,S);
 

array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
array( 1 .. 20, 1 .. 20, [( 1, 8 ) = 0, ( 19, 4 ) = 0, ( 6, 12 ) = 0, ( 7, 18 ) = 0, ( 18, 7 ) = 0, ( 1, 4 ) = 0, ( 2, 4 ) = 0, ( 12, 6 ) = 0, ( 10, 14 ) = 0, ( 5, 20 ) = 0, ( 9, 14 ) = 0, ( 17, 9 ) =...
(29)
 

> mat:=evalm(S&*exponential(J,zeta)&*inverse(S)):
 

> mat1:=evalm(subs(zeta=zeta-zeta1,evalm(mat))):
 

> b2:=evalm(subs(zeta=zeta1,evalm(b))):
 

> mat2:=evalm(mat1&*b2):
 

> mat2:=map(expand,mat2):
 

> mat3:=map(int,mat2,zeta1=0..zeta):
 

> Y0:=matrix(2*N,1);
 

array( 1 .. 20, 1 .. 1, [ ] ) (30)
 

> for i to N do Y0[i,1]:=p[i];od:
 

> for i to N do Y0[N+i,1]:=c[i]:od:
 

> evalm(Y0);
 

array( 1 .. 20, 1 .. 1, [( 10, 1 ) = p[10], ( 5, 1 ) = p[5], ( 14, 1 ) = c[4], ( 12, 1 ) = c[2], ( 15, 1 ) = c[5], ( 18, 1 ) = c[8], ( 9, 1 ) = p[9], ( 6, 1 ) = p[6], ( 2, 1 ) = p[2], ( 7, 1 ) = p[7],... (31)
 

> Y:=evalm(mat&*Y0+mat3):
 

> sol0:=map(eval,evalm(subs(zeta=0,evalm(Y)))):
 

> sol1:=map(eval,evalm(subs(zeta=epsilon/h,evalm(Y)))):
 

> 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;
 

 

 

 

 

 

 

 

 

 

p[1]
p[2]
p[3]
p[4]
p[5]
p[6]
p[7]
p[8]
p[9]
p[10] (32)
 

> 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;
 

 

 

 

 

 

 

 

 

 

`+`(`*`(95085203.27, `*`(p[1])), `-`(`*`(145993439.6, `*`(p[2]))), `*`(141208835.7, `*`(p[3])), `-`(`*`(102223000.8, `*`(p[4]))), `*`(58692046.46, `*`(p[5])), `-`(`*`(27485386.94, `*`(p[6]))), `*`(106...
`+`(`*`(95085203.27, `*`(p[1])), `-`(`*`(145993439.6, `*`(p[2]))), `*`(141208835.7, `*`(p[3])), `-`(`*`(102223000.8, `*`(p[4]))), `*`(58692046.46, `*`(p[5])), `-`(`*`(27485386.94, `*`(p[6]))), `*`(106...
`+`(`*`(95085203.27, `*`(p[1])), `-`(`*`(145993439.6, `*`(p[2]))), `*`(141208835.7, `*`(p[3])), `-`(`*`(102223000.8, `*`(p[4]))), `*`(58692046.46, `*`(p[5])), `-`(`*`(27485386.94, `*`(p[6]))), `*`(106...
`+`(`*`(95085203.27, `*`(p[1])), `-`(`*`(145993439.6, `*`(p[2]))), `*`(141208835.7, `*`(p[3])), `-`(`*`(102223000.8, `*`(p[4]))), `*`(58692046.46, `*`(p[5])), `-`(`*`(27485386.94, `*`(p[6]))), `*`(106...
`+`(`*`(95085203.27, `*`(p[1])), `-`(`*`(145993439.6, `*`(p[2]))), `*`(141208835.7, `*`(p[3])), `-`(`*`(102223000.8, `*`(p[4]))), `*`(58692046.46, `*`(p[5])), `-`(`*`(27485386.94, `*`(p[6]))), `*`(106...
`+`(`-`(`*`(145967191.5, `*`(p[1]))), `*`(236293587.1, `*`(p[2])), `-`(`*`(248262926.7, `*`(p[3]))), `*`(199841166.3, `*`(p[4])), `-`(`*`(129704287.5, `*`(p[5]))), `*`(69373712.68, `*`(p[6])), `-`(`*`...
`+`(`-`(`*`(145967191.5, `*`(p[1]))), `*`(236293587.1, `*`(p[2])), `-`(`*`(248262926.7, `*`(p[3]))), `*`(199841166.3, `*`(p[4])), `-`(`*`(129704287.5, `*`(p[5]))), `*`(69373712.68, `*`(p[6])), `-`(`*`...
`+`(`-`(`*`(145967191.5, `*`(p[1]))), `*`(236293587.1, `*`(p[2])), `-`(`*`(248262926.7, `*`(p[3]))), `*`(199841166.3, `*`(p[4])), `-`(`*`(129704287.5, `*`(p[5]))), `*`(69373712.68, `*`(p[6])), `-`(`*`...
`+`(`-`(`*`(145967191.5, `*`(p[1]))), `*`(236293587.1, `*`(p[2])), `-`(`*`(248262926.7, `*`(p[3]))), `*`(199841166.3, `*`(p[4])), `-`(`*`(129704287.5, `*`(p[5]))), `*`(69373712.68, `*`(p[6])), `-`(`*`...
`+`(`-`(`*`(145967191.5, `*`(p[1]))), `*`(236293587.1, `*`(p[2])), `-`(`*`(248262926.7, `*`(p[3]))), `*`(199841166.3, `*`(p[4])), `-`(`*`(129704287.5, `*`(p[5]))), `*`(69373712.68, `*`(p[6])), `-`(`*`...
`+`(`*`(141161293.2, `*`(p[1])), `-`(`*`(248243204.3, `*`(p[2]))), `*`(295025857.1, `*`(p[3])), `-`(`*`(275679007.9, `*`(p[4]))), `*`(210559084.8, `*`(p[5])), `-`(`*`(133220354.1, `*`(p[6]))), `*`(703...
`+`(`*`(141161293.2, `*`(p[1])), `-`(`*`(248243204.3, `*`(p[2]))), `*`(295025857.1, `*`(p[3])), `-`(`*`(275679007.9, `*`(p[4]))), `*`(210559084.8, `*`(p[5])), `-`(`*`(133220354.1, `*`(p[6]))), `*`(703...
`+`(`*`(141161293.2, `*`(p[1])), `-`(`*`(248243204.3, `*`(p[2]))), `*`(295025857.1, `*`(p[3])), `-`(`*`(275679007.9, `*`(p[4]))), `*`(210559084.8, `*`(p[5])), `-`(`*`(133220354.1, `*`(p[6]))), `*`(703...
`+`(`*`(141161293.2, `*`(p[1])), `-`(`*`(248243204.3, `*`(p[2]))), `*`(295025857.1, `*`(p[3])), `-`(`*`(275679007.9, `*`(p[4]))), `*`(210559084.8, `*`(p[5])), `-`(`*`(133220354.1, `*`(p[6]))), `*`(703...
`+`(`*`(141161293.2, `*`(p[1])), `-`(`*`(248243204.3, `*`(p[2]))), `*`(295025857.1, `*`(p[3])), `-`(`*`(275679007.9, `*`(p[4]))), `*`(210559084.8, `*`(p[5])), `-`(`*`(133220354.1, `*`(p[6]))), `*`(703...
`+`(`-`(`*`(102221840.0, `*`(p[1]))), `*`(199900105.4, `*`(p[2])), `-`(`*`(275756279.3, `*`(p[3]))), `*`(305641110.5, `*`(p[4])), `-`(`*`(279208245.2, `*`(p[5]))), `*`(211545113.2, `*`(p[6])), `-`(`*`...
`+`(`-`(`*`(102221840.0, `*`(p[1]))), `*`(199900105.4, `*`(p[2])), `-`(`*`(275756279.3, `*`(p[3]))), `*`(305641110.5, `*`(p[4])), `-`(`*`(279208245.2, `*`(p[5]))), `*`(211545113.2, `*`(p[6])), `-`(`*`...
`+`(`-`(`*`(102221840.0, `*`(p[1]))), `*`(199900105.4, `*`(p[2])), `-`(`*`(275756279.3, `*`(p[3]))), `*`(305641110.5, `*`(p[4])), `-`(`*`(279208245.2, `*`(p[5]))), `*`(211545113.2, `*`(p[6])), `-`(`*`...
`+`(`-`(`*`(102221840.0, `*`(p[1]))), `*`(199900105.4, `*`(p[2])), `-`(`*`(275756279.3, `*`(p[3]))), `*`(305641110.5, `*`(p[4])), `-`(`*`(279208245.2, `*`(p[5]))), `*`(211545113.2, `*`(p[6])), `-`(`*`...
`+`(`-`(`*`(102221840.0, `*`(p[1]))), `*`(199900105.4, `*`(p[2])), `-`(`*`(275756279.3, `*`(p[3]))), `*`(305641110.5, `*`(p[4])), `-`(`*`(279208245.2, `*`(p[5]))), `*`(211545113.2, `*`(p[6])), `-`(`*`...
`+`(`*`(58681626.67, `*`(p[1])), `-`(`*`(129737170.0, `*`(p[2]))), `*`(210596014.5, `*`(p[3])), `-`(`*`(279187893.6, `*`(p[4]))), `*`(306640168.0, `*`(p[5])), `-`(`*`(279439564.8, `*`(p[6]))), `*`(211...
`+`(`*`(58681626.67, `*`(p[1])), `-`(`*`(129737170.0, `*`(p[2]))), `*`(210596014.5, `*`(p[3])), `-`(`*`(279187893.6, `*`(p[4]))), `*`(306640168.0, `*`(p[5])), `-`(`*`(279439564.8, `*`(p[6]))), `*`(211...
`+`(`*`(58681626.67, `*`(p[1])), `-`(`*`(129737170.0, `*`(p[2]))), `*`(210596014.5, `*`(p[3])), `-`(`*`(279187893.6, `*`(p[4]))), `*`(306640168.0, `*`(p[5])), `-`(`*`(279439564.8, `*`(p[6]))), `*`(211...
`+`(`*`(58681626.67, `*`(p[1])), `-`(`*`(129737170.0, `*`(p[2]))), `*`(210596014.5, `*`(p[3])), `-`(`*`(279187893.6, `*`(p[4]))), `*`(306640168.0, `*`(p[5])), `-`(`*`(279439564.8, `*`(p[6]))), `*`(211...
`+`(`*`(58681626.67, `*`(p[1])), `-`(`*`(129737170.0, `*`(p[2]))), `*`(210596014.5, `*`(p[3])), `-`(`*`(279187893.6, `*`(p[4]))), `*`(306640168.0, `*`(p[5])), `-`(`*`(279439564.8, `*`(p[6]))), `*`(211...
`+`(`-`(`*`(27473537.32, `*`(p[1]))), `*`(69389569.39, `*`(p[2])), `-`(`*`(133234518.5, `*`(p[3]))), `*`(211523203.8, `*`(p[4])), `-`(`*`(279433895.0, `*`(p[5]))), `*`(306644436.0, `*`(p[6])), `-`(`*`...
`+`(`-`(`*`(27473537.32, `*`(p[1]))), `*`(69389569.39, `*`(p[2])), `-`(`*`(133234518.5, `*`(p[3]))), `*`(211523203.8, `*`(p[4])), `-`(`*`(279433895.0, `*`(p[5]))), `*`(306644436.0, `*`(p[6])), `-`(`*`...
`+`(`-`(`*`(27473537.32, `*`(p[1]))), `*`(69389569.39, `*`(p[2])), `-`(`*`(133234518.5, `*`(p[3]))), `*`(211523203.8, `*`(p[4])), `-`(`*`(279433895.0, `*`(p[5]))), `*`(306644436.0, `*`(p[6])), `-`(`*`...
`+`(`-`(`*`(27473537.32, `*`(p[1]))), `*`(69389569.39, `*`(p[2])), `-`(`*`(133234518.5, `*`(p[3]))), `*`(211523203.8, `*`(p[4])), `-`(`*`(279433895.0, `*`(p[5]))), `*`(306644436.0, `*`(p[6])), `-`(`*`...
`+`(`-`(`*`(27473537.32, `*`(p[1]))), `*`(69389569.39, `*`(p[2])), `-`(`*`(133234518.5, `*`(p[3]))), `*`(211523203.8, `*`(p[4])), `-`(`*`(279433895.0, `*`(p[5]))), `*`(306644436.0, `*`(p[6])), `-`(`*`...
`+`(`*`(10679149.13, `*`(p[1])), `-`(`*`(30982435.46, `*`(p[2]))), `*`(70358662.9, `*`(p[3])), `-`(`*`(133432516.8, `*`(p[4]))), `*`(211539125.4, `*`(p[5])), `-`(`*`(279213456.4, `*`(p[6]))), `*`(3056...
`+`(`*`(10679149.13, `*`(p[1])), `-`(`*`(30982435.46, `*`(p[2]))), `*`(70358662.9, `*`(p[3])), `-`(`*`(133432516.8, `*`(p[4]))), `*`(211539125.4, `*`(p[5])), `-`(`*`(279213456.4, `*`(p[6]))), `*`(3056...
`+`(`*`(10679149.13, `*`(p[1])), `-`(`*`(30982435.46, `*`(p[2]))), `*`(70358662.9, `*`(p[3])), `-`(`*`(133432516.8, `*`(p[4]))), `*`(211539125.4, `*`(p[5])), `-`(`*`(279213456.4, `*`(p[6]))), `*`(3056...
`+`(`*`(10679149.13, `*`(p[1])), `-`(`*`(30982435.46, `*`(p[2]))), `*`(70358662.9, `*`(p[3])), `-`(`*`(133432516.8, `*`(p[4]))), `*`(211539125.4, `*`(p[5])), `-`(`*`(279213456.4, `*`(p[6]))), `*`(3056...
`+`(`*`(10679149.13, `*`(p[1])), `-`(`*`(30982435.46, `*`(p[2]))), `*`(70358662.9, `*`(p[3])), `-`(`*`(133432516.8, `*`(p[4]))), `*`(211539125.4, `*`(p[5])), `-`(`*`(279213456.4, `*`(p[6]))), `*`(3056...
`+`(`-`(`*`(3491933.48, `*`(p[1]))), `*`(11657542.5, `*`(p[2])), `-`(`*`(31203327.0, `*`(p[3]))), `*`(70345923.1, `*`(p[4])), `-`(`*`(133218957.5, `*`(p[5]))), `*`(210571444.0, `*`(p[6])), `-`(`*`(275...
`+`(`-`(`*`(3491933.48, `*`(p[1]))), `*`(11657542.5, `*`(p[2])), `-`(`*`(31203327.0, `*`(p[3]))), `*`(70345923.1, `*`(p[4])), `-`(`*`(133218957.5, `*`(p[5]))), `*`(210571444.0, `*`(p[6])), `-`(`*`(275...
`+`(`-`(`*`(3491933.48, `*`(p[1]))), `*`(11657542.5, `*`(p[2])), `-`(`*`(31203327.0, `*`(p[3]))), `*`(70345923.1, `*`(p[4])), `-`(`*`(133218957.5, `*`(p[5]))), `*`(210571444.0, `*`(p[6])), `-`(`*`(275...
`+`(`-`(`*`(3491933.48, `*`(p[1]))), `*`(11657542.5, `*`(p[2])), `-`(`*`(31203327.0, `*`(p[3]))), `*`(70345923.1, `*`(p[4])), `-`(`*`(133218957.5, `*`(p[5]))), `*`(210571444.0, `*`(p[6])), `-`(`*`(275...
`+`(`-`(`*`(3491933.48, `*`(p[1]))), `*`(11657542.5, `*`(p[2])), `-`(`*`(31203327.0, `*`(p[3]))), `*`(70345923.1, `*`(p[4])), `-`(`*`(133218957.5, `*`(p[5]))), `*`(210571444.0, `*`(p[6])), `-`(`*`(275...
`+`(`*`(969625.40, `*`(p[1])), `-`(`*`(3718956.2, `*`(p[2]))), `*`(11655659.5, `*`(p[3])), `-`(`*`(30974568.19, `*`(p[4]))), `*`(69380928.16, `*`(p[5])), `-`(`*`(129727519.2, `*`(p[6]))), `*`(19989076...
`+`(`*`(969625.40, `*`(p[1])), `-`(`*`(3718956.2, `*`(p[2]))), `*`(11655659.5, `*`(p[3])), `-`(`*`(30974568.19, `*`(p[4]))), `*`(69380928.16, `*`(p[5])), `-`(`*`(129727519.2, `*`(p[6]))), `*`(19989076...
`+`(`*`(969625.40, `*`(p[1])), `-`(`*`(3718956.2, `*`(p[2]))), `*`(11655659.5, `*`(p[3])), `-`(`*`(30974568.19, `*`(p[4]))), `*`(69380928.16, `*`(p[5])), `-`(`*`(129727519.2, `*`(p[6]))), `*`(19989076...
`+`(`*`(969625.40, `*`(p[1])), `-`(`*`(3718956.2, `*`(p[2]))), `*`(11655659.5, `*`(p[3])), `-`(`*`(30974568.19, `*`(p[4]))), `*`(69380928.16, `*`(p[5])), `-`(`*`(129727519.2, `*`(p[6]))), `*`(19989076...
`+`(`*`(969625.40, `*`(p[1])), `-`(`*`(3718956.2, `*`(p[2]))), `*`(11655659.5, `*`(p[3])), `-`(`*`(30974568.19, `*`(p[4]))), `*`(69380928.16, `*`(p[5])), `-`(`*`(129727519.2, `*`(p[6]))), `*`(19989076...
`+`(`-`(`*`(223082.04, `*`(p[1]))), `*`(971062.48, `*`(p[2])), `-`(`*`(3494542.02, `*`(p[3]))), `*`(10683265.04, `*`(p[4])), `-`(`*`(27483049.23, `*`(p[5]))), `*`(58698469.50, `*`(p[6])), `-`(`*`(1022...
`+`(`-`(`*`(223082.04, `*`(p[1]))), `*`(971062.48, `*`(p[2])), `-`(`*`(3494542.02, `*`(p[3]))), `*`(10683265.04, `*`(p[4])), `-`(`*`(27483049.23, `*`(p[5]))), `*`(58698469.50, `*`(p[6])), `-`(`*`(1022...
`+`(`-`(`*`(223082.04, `*`(p[1]))), `*`(971062.48, `*`(p[2])), `-`(`*`(3494542.02, `*`(p[3]))), `*`(10683265.04, `*`(p[4])), `-`(`*`(27483049.23, `*`(p[5]))), `*`(58698469.50, `*`(p[6])), `-`(`*`(1022...
`+`(`-`(`*`(223082.04, `*`(p[1]))), `*`(971062.48, `*`(p[2])), `-`(`*`(3494542.02, `*`(p[3]))), `*`(10683265.04, `*`(p[4])), `-`(`*`(27483049.23, `*`(p[5]))), `*`(58698469.50, `*`(p[6])), `-`(`*`(1022...
`+`(`-`(`*`(223082.04, `*`(p[1]))), `*`(971062.48, `*`(p[2])), `-`(`*`(3494542.02, `*`(p[3]))), `*`(10683265.04, `*`(p[4])), `-`(`*`(27483049.23, `*`(p[5]))), `*`(58698469.50, `*`(p[6])), `-`(`*`(1022...
(33)
 

> csol:=solve({seq(Eq[i],i=1..2*N)},{seq(c[i],i=1..N),seq(p[i],i=1..N)});
 

{c[7] = 0.2855670636e-1, c[10] = 0.8886578634e-2, c[3] = 0.2369154365e-1, c[1] = 0.8923567879e-2, p[5] = 0., p[4] = 0., p[7] = 0., p[9] = 0., p[8] = 0., p[1] = 0., p[2] = 0., p[3] = 0., c[6] = 0.30999...
{c[7] = 0.2855670636e-1, c[10] = 0.8886578634e-2, c[3] = 0.2369154365e-1, c[1] = 0.8923567879e-2, p[5] = 0., p[4] = 0., p[7] = 0., p[9] = 0., p[8] = 0., p[1] = 0., p[2] = 0., p[3] = 0., c[6] = 0.30999...
{c[7] = 0.2855670636e-1, c[10] = 0.8886578634e-2, c[3] = 0.2369154365e-1, c[1] = 0.8923567879e-2, p[5] = 0., p[4] = 0., p[7] = 0., p[9] = 0., p[8] = 0., p[1] = 0., p[2] = 0., p[3] = 0., c[6] = 0.30999...
(34)
 

> assign(csol);
 

> Y:=map(eval,Y):
 

> for i from 1 to N do u[i](zeta):=eval((Y[i,1]));od:
 

> for i from 0 to N+1 do u[i](zeta):=eval(u[i](zeta));od:
 

> for i from 0 to N+1 do u[i](y):=eval(subs(zeta=epsilon*y/h,u[i](zeta)));od;
 

 

 

 

 

 

 

 

 

 

 

 

0
`+`(`-`(`*`(0.807e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.1421032e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.2e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(...
`+`(`-`(`*`(0.807e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.1421032e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.2e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(...
`+`(`-`(`*`(0.807e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.1421032e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.2e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(...
`+`(`-`(`*`(0.807e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.1421032e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.2e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(...
`+`(`-`(`*`(0.807e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.1421032e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.2e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(...
`+`(`-`(`*`(0.807e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.1421032e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.2e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(...
`+`(`-`(`*`(0.807e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.1421032e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.2e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(...
`+`(`*`(0.2222e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.3748953e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.5e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.3996201...
`+`(`*`(0.2222e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.3748953e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.5e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.3996201...
`+`(`*`(0.2222e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.3748953e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.5e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.3996201...
`+`(`*`(0.2222e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.3748953e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.5e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.3996201...
`+`(`*`(0.2222e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.3748953e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.5e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.3996201...
`+`(`*`(0.2222e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.3748953e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.5e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.3996201...
`+`(`*`(0.2222e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.3748953e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.5e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.3996201...
`+`(`*`(0.740e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.43945214e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.3e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(0.55...
`+`(`*`(0.740e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.43945214e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.3e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(0.55...
`+`(`*`(0.740e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.43945214e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.3e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(0.55...
`+`(`*`(0.740e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.43945214e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.3e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(0.55...
`+`(`*`(0.740e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.43945214e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.3e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(0.55...
`+`(`*`(0.740e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.43945214e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.3e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(0.55...
`+`(`*`(0.740e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.43945214e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.3e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(0.55...
`+`(`-`(`*`(0.447e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.54121551e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.8e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.66...
`+`(`-`(`*`(0.447e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.54121551e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.8e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.66...
`+`(`-`(`*`(0.447e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.54121551e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.8e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.66...
`+`(`-`(`*`(0.447e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.54121551e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.8e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.66...
`+`(`-`(`*`(0.447e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.54121551e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.8e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.66...
`+`(`-`(`*`(0.447e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.54121551e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.8e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.66...
`+`(`-`(`*`(0.447e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.54121551e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.8e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.66...
`+`(`-`(`*`(0.613e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.6382298e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.8e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(...
`+`(`-`(`*`(0.613e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.6382298e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.8e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(...
`+`(`-`(`*`(0.613e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.6382298e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.8e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(...
`+`(`-`(`*`(0.613e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.6382298e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.8e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(...
`+`(`-`(`*`(0.613e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.6382298e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.8e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(...
`+`(`-`(`*`(0.613e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.6382298e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.8e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(...
`+`(`-`(`*`(0.613e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.6382298e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.8e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(...
`+`(`*`(0.620e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.5609990e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.9e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.7234989e...
`+`(`*`(0.620e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.5609990e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.9e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.7234989e...
`+`(`*`(0.620e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.5609990e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.9e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.7234989e...
`+`(`*`(0.620e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.5609990e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.9e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.7234989e...
`+`(`*`(0.620e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.5609990e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.9e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.7234989e...
`+`(`*`(0.620e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.5609990e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.9e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.7234989e...
`+`(`*`(0.620e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.5609990e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.9e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.7234989e...
`+`(`*`(0.432e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.56514689e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.9e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(0.66...
`+`(`*`(0.432e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.56514689e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.9e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(0.66...
`+`(`*`(0.432e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.56514689e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.9e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(0.66...
`+`(`*`(0.432e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.56514689e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.9e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(0.66...
`+`(`*`(0.432e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.56514689e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.9e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(0.66...
`+`(`*`(0.432e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.56514689e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.9e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(0.66...
`+`(`*`(0.432e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.56514689e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.9e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*`(0.66...
`+`(`-`(`*`(0.761e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.48539085e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.2e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.55...
`+`(`-`(`*`(0.761e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.48539085e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.2e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.55...
`+`(`-`(`*`(0.761e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.48539085e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.2e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.55...
`+`(`-`(`*`(0.761e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.48539085e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.2e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.55...
`+`(`-`(`*`(0.761e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.48539085e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.2e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.55...
`+`(`-`(`*`(0.761e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.48539085e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.2e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.55...
`+`(`-`(`*`(0.761e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.48539085e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.2e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.55...
`+`(`-`(`*`(0.2339e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.2908464e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.10e-11, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*...
`+`(`-`(`*`(0.2339e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.2908464e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.10e-11, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*...
`+`(`-`(`*`(0.2339e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.2908464e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.10e-11, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*...
`+`(`-`(`*`(0.2339e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.2908464e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.10e-11, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*...
`+`(`-`(`*`(0.2339e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.2908464e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.10e-11, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*...
`+`(`-`(`*`(0.2339e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.2908464e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.10e-11, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*...
`+`(`-`(`*`(0.2339e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y))))))), `-`(`*`(0.2908464e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `-`(`*`(0.10e-11, `*`(exp(`+`(`*`(21.77604411, `*`(y))))))), `*...
`+`(`*`(0.806e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.2063057e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.3e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.2092455e...
`+`(`*`(0.806e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.2063057e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.3e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.2092455e...
`+`(`*`(0.806e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.2063057e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.3e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.2092455e...
`+`(`*`(0.806e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.2063057e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.3e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.2092455e...
`+`(`*`(0.806e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.2063057e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.3e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.2092455e...
`+`(`*`(0.806e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.2063057e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.3e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.2092455e...
`+`(`*`(0.806e-10, `*`(exp(`+`(`*`(16.62646795, `*`(y)))))), `-`(`*`(0.2063057e-5, `*`(exp(`+`(`-`(`*`(20.01181689, `*`(y)))))))), `*`(0.3e-12, `*`(exp(`+`(`*`(21.77604411, `*`(y)))))), `*`(0.2092455e...
0 (35)
 

> for i from 0 to N+1 do
 pl[i]:=line([0.3,0.98-abs(i-5.25)*0.14],[0.6,evalf(subs(y=0.6,u[i](y)))],thickness=1,linestyle=dot);
 pt[i]:=textplot([0.3,0.98-abs(i-5.25)*0.14,typeset(u[i],"(y)")],align=left):
end do:
 

> pp:=plot([seq(u[i](y),i=0..N+1)],y=0..1);
 

PLOT(CURVES([[0., 0.], [0.217971541666666658e-1, 0.], [0.407627414583333348e-1, 0.], [0.620915279166666667e-1, 0.], [0.835616954166666648e-1, 0.], [.104929818958333324, 0.], [.124740804791666660, 0.],... (36)
 

> display([pp,seq(pl[i],i=0..N+1),seq(pt[i],i=0..N+1)],axes=boxed,thickness=3,title="Figure Exp. 6.1.",labels=[y,"u"]);
 

Plot_2d
 

> M:=10;
 

10 (37)
 

> T1:=[seq(evalf(i/M),i=0..M)];
 

[0., .1000000000, .2000000000, .3000000000, .4000000000, .5000000000, .6000000000, .7000000000, .8000000000, .9000000000, 1.]
[0., .1000000000, .2000000000, .3000000000, .4000000000, .5000000000, .6000000000, .7000000000, .8000000000, .9000000000, 1.]
(38)
 

> 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:
 

> P[M+1]:=plot([seq([h*i,evalf(subs(x=i*h,1))],i=0..N+1)],style=line,thickness=3,title="Figure Exp. 6.2.",axes=boxed):
 

> for j from 1 to M+1 do
 pt[j]:=textplot([0.5,evalf(subs(y=T1[j],u[5](y))),typeset(y,sprintf("=%4.2f",T1[j]))],align=above);
od:
 

> display({seq(P[i],i=1..M+1),seq(pt[j],j=1..M+1)},labels=[x,u]);
 

Plot_2d
 

> Ny:=30;
 

30 (39)
 

> PP:=matrix(N+2,Ny);
 

array( 1 .. 12, 1 .. 30, [ ] ) (40)
 

> for i to Ny do PP[1,i]:=0;PP[N+2,i]:=0;od:
 

> for i to N+2 do PP[i,1]:=0;PP[i,Ny]:=1;od:
 

> for i from 2 to N+1 do for j from 2 to Ny-1 do PP[i,j]:=evalf(subs(y=(j-1)/(Ny-1),u[i-1](y)));od;od:
 

> plotdata := [seq([ seq([(i-1)/(N+1),(j-1)/(Ny-1),PP[i,j]], i=1..N+2)], j=1..Ny)]:
 

> surfdata(plotdata,axes=boxed,title="Figure Exp. 6.3.",labels=[x,y,u],orientation=[-120,60] );
 

Plot
 

>