Example 3.8b  Cylindrical Catalyst Pellet 

> restart:
 

> with(linalg):with(plots):
 

> N:=10;
 

10 (1)
 

> L:=1;
 

1 (2)
 

> eq:=diff(y(x),x$2)+1/x*diff(y(x),x)-phi^2*y(x);
 

`+`(diff(diff(y(x), x), x), `/`(`*`(diff(y(x), x)), `*`(x)), `-`(`*`(`^`(phi, 2), `*`(y(x))))) (3)
 

> bc1:=diff(y(x),x);
 

diff(y(x), x) (4)
 

> bc2:=diff(y(x),x)-1+y(x);
 

`+`(diff(y(x), x), `-`(1), y(x)) (5)
 

The central difference expression for the second and first derivatives are 

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

`/`(`*`(`+`(y[`+`(m, 1)], `-`(`*`(2, `*`(y[m]))), y[`+`(m, `-`(1))])), `*`(`^`(h, 2))) (6)
 

> dydx:=(y[m+1]-y[m-1])/2/h;
 

`+`(`/`(`*`(`/`(1, 2), `*`(`+`(y[`+`(m, 1)], `-`(y[`+`(m, `-`(1))])))), `*`(h))) (7)
 

The three point forward and backward difference expressions for the derivative are: 

> dydxf:=(-y[2]+4*y[1]-3*y[0])/(2*h);
 

`+`(`/`(`*`(`/`(1, 2), `*`(`+`(`-`(y[2]), `*`(4, `*`(y[1])), `-`(`*`(3, `*`(y[0])))))), `*`(h))) (8)
 

> dydxb:=(y[N-1]-4*y[N]+3*y[N+1])/(2*h);
 

`+`(`/`(`*`(`/`(1, 2), `*`(`+`(y[9], `-`(`*`(4, `*`(y[10]))), `*`(3, `*`(y[11]))))), `*`(h))) (9)
 

The governing equation in finite difference form is: 

> Eq[m]:=subs(diff(y(x),x$2)=d2ydx2,diff(y(x),x)=dydx,y(x)=y[m],x=m*h,eq);
 

`+`(`/`(`*`(`+`(y[`+`(m, 1)], `-`(`*`(2, `*`(y[m]))), y[`+`(m, `-`(1))])), `*`(`^`(h, 2))), `/`(`*`(`/`(1, 2), `*`(`+`(y[`+`(m, 1)], `-`(y[`+`(m, `-`(1))])))), `*`(m, `*`(`^`(h, 2)))), `-`(`*`(`^`(phi... (10)
 

The boundary conditions in finite difference form are: 

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

`+`(`/`(`*`(`/`(1, 2), `*`(`+`(`-`(y[2]), `*`(4, `*`(y[1])), `-`(`*`(3, `*`(y[0])))))), `*`(h))) (11)
 

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

`+`(`/`(`*`(`/`(1, 2), `*`(`+`(y[9], `-`(`*`(4, `*`(y[10]))), `*`(3, `*`(y[11]))))), `*`(h)), `-`(1), y[11]) (12)
 

A 'for loop' can be written for the interior node points as 

> for i to N do Eq[i]:=subs(m=i,Eq[m]);od;
 

 

 

 

 

 

 

 

 

 

`+`(`/`(`*`(`+`(y[2], `-`(`*`(2, `*`(y[1]))), y[0])), `*`(`^`(h, 2))), `/`(`*`(`/`(1, 2), `*`(`+`(y[2], `-`(y[0])))), `*`(`^`(h, 2))), `-`(`*`(`^`(phi, 2), `*`(y[1]))))
`+`(`/`(`*`(`+`(y[3], `-`(`*`(2, `*`(y[2]))), y[1])), `*`(`^`(h, 2))), `/`(`*`(`/`(1, 4), `*`(`+`(y[3], `-`(y[1])))), `*`(`^`(h, 2))), `-`(`*`(`^`(phi, 2), `*`(y[2]))))
`+`(`/`(`*`(`+`(y[4], `-`(`*`(2, `*`(y[3]))), y[2])), `*`(`^`(h, 2))), `/`(`*`(`/`(1, 6), `*`(`+`(y[4], `-`(y[2])))), `*`(`^`(h, 2))), `-`(`*`(`^`(phi, 2), `*`(y[3]))))
`+`(`/`(`*`(`+`(y[5], `-`(`*`(2, `*`(y[4]))), y[3])), `*`(`^`(h, 2))), `/`(`*`(`/`(1, 8), `*`(`+`(y[5], `-`(y[3])))), `*`(`^`(h, 2))), `-`(`*`(`^`(phi, 2), `*`(y[4]))))
`+`(`/`(`*`(`+`(y[6], `-`(`*`(2, `*`(y[5]))), y[4])), `*`(`^`(h, 2))), `/`(`*`(`/`(1, 10), `*`(`+`(y[6], `-`(y[4])))), `*`(`^`(h, 2))), `-`(`*`(`^`(phi, 2), `*`(y[5]))))
`+`(`/`(`*`(`+`(y[7], `-`(`*`(2, `*`(y[6]))), y[5])), `*`(`^`(h, 2))), `/`(`*`(`/`(1, 12), `*`(`+`(y[7], `-`(y[5])))), `*`(`^`(h, 2))), `-`(`*`(`^`(phi, 2), `*`(y[6]))))
`+`(`/`(`*`(`+`(y[8], `-`(`*`(2, `*`(y[7]))), y[6])), `*`(`^`(h, 2))), `/`(`*`(`/`(1, 14), `*`(`+`(y[8], `-`(y[6])))), `*`(`^`(h, 2))), `-`(`*`(`^`(phi, 2), `*`(y[7]))))
`+`(`/`(`*`(`+`(y[9], `-`(`*`(2, `*`(y[8]))), y[7])), `*`(`^`(h, 2))), `/`(`*`(`/`(1, 16), `*`(`+`(y[9], `-`(y[7])))), `*`(`^`(h, 2))), `-`(`*`(`^`(phi, 2), `*`(y[8]))))
`+`(`/`(`*`(`+`(y[10], `-`(`*`(2, `*`(y[9]))), y[8])), `*`(`^`(h, 2))), `/`(`*`(`/`(1, 18), `*`(`+`(y[10], `-`(y[8])))), `*`(`^`(h, 2))), `-`(`*`(`^`(phi, 2), `*`(y[9]))))
`+`(`/`(`*`(`+`(y[11], `-`(`*`(2, `*`(y[10]))), y[9])), `*`(`^`(h, 2))), `/`(`*`(`/`(1, 20), `*`(`+`(y[11], `-`(y[9])))), `*`(`^`(h, 2))), `-`(`*`(`^`(phi, 2), `*`(y[10])))) (13)
 

> y[0]:=solve(Eq[0],y[0]);
 

`+`(`-`(`*`(`/`(1, 3), `*`(y[2]))), `*`(`/`(4, 3), `*`(y[1]))) (14)
 

> y[N+1]:=solve(Eq[N+1],y[N+1]);
 

`/`(`*`(`+`(`-`(y[9]), `*`(4, `*`(y[10])), `*`(2, `*`(h)))), `*`(`+`(3, `*`(2, `*`(h))))) (15)
 

> h:=L/(N+1);
 

`/`(1, 11) (16)
 

> for i to N do Eq[i]:=eval(Eq[i]);od;
 

 

 

 

 

 

 

 

 

 

`+`(`*`(`/`(484, 3), `*`(y[2])), `-`(`*`(`/`(484, 3), `*`(y[1]))), `-`(`*`(`^`(phi, 2), `*`(y[1]))))
`+`(`*`(`/`(605, 4), `*`(y[3])), `-`(`*`(242, `*`(y[2]))), `*`(`/`(363, 4), `*`(y[1])), `-`(`*`(`^`(phi, 2), `*`(y[2]))))
`+`(`*`(`/`(847, 6), `*`(y[4])), `-`(`*`(242, `*`(y[3]))), `*`(`/`(605, 6), `*`(y[2])), `-`(`*`(`^`(phi, 2), `*`(y[3]))))
`+`(`*`(`/`(1089, 8), `*`(y[5])), `-`(`*`(242, `*`(y[4]))), `*`(`/`(847, 8), `*`(y[3])), `-`(`*`(`^`(phi, 2), `*`(y[4]))))
`+`(`*`(`/`(1331, 10), `*`(y[6])), `-`(`*`(242, `*`(y[5]))), `*`(`/`(1089, 10), `*`(y[4])), `-`(`*`(`^`(phi, 2), `*`(y[5]))))
`+`(`*`(`/`(1573, 12), `*`(y[7])), `-`(`*`(242, `*`(y[6]))), `*`(`/`(1331, 12), `*`(y[5])), `-`(`*`(`^`(phi, 2), `*`(y[6]))))
`+`(`*`(`/`(1815, 14), `*`(y[8])), `-`(`*`(242, `*`(y[7]))), `*`(`/`(1573, 14), `*`(y[6])), `-`(`*`(`^`(phi, 2), `*`(y[7]))))
`+`(`*`(`/`(2057, 16), `*`(y[9])), `-`(`*`(242, `*`(y[8]))), `*`(`/`(1815, 16), `*`(y[7])), `-`(`*`(`^`(phi, 2), `*`(y[8]))))
`+`(`*`(`/`(2299, 18), `*`(y[10])), `-`(`*`(242, `*`(y[9]))), `*`(`/`(2057, 18), `*`(y[8])), `-`(`*`(`^`(phi, 2), `*`(y[9]))))
`+`(`*`(`/`(3751, 50), `*`(y[9])), `-`(`*`(`/`(2057, 25), `*`(y[10]))), `/`(363, 50), `-`(`*`(`^`(phi, 2), `*`(y[10])))) (17)
 

> eqs:=[seq(Eq[i],i=1..N)];
 

[`+`(`*`(`/`(484, 3), `*`(y[2])), `-`(`*`(`/`(484, 3), `*`(y[1]))), `-`(`*`(`^`(phi, 2), `*`(y[1])))), `+`(`*`(`/`(605, 4), `*`(y[3])), `-`(`*`(242, `*`(y[2]))), `*`(`/`(363, 4), `*`(y[1])), `-`(`*`(`...
[`+`(`*`(`/`(484, 3), `*`(y[2])), `-`(`*`(`/`(484, 3), `*`(y[1]))), `-`(`*`(`^`(phi, 2), `*`(y[1])))), `+`(`*`(`/`(605, 4), `*`(y[3])), `-`(`*`(242, `*`(y[2]))), `*`(`/`(363, 4), `*`(y[1])), `-`(`*`(`...
[`+`(`*`(`/`(484, 3), `*`(y[2])), `-`(`*`(`/`(484, 3), `*`(y[1]))), `-`(`*`(`^`(phi, 2), `*`(y[1])))), `+`(`*`(`/`(605, 4), `*`(y[3])), `-`(`*`(242, `*`(y[2]))), `*`(`/`(363, 4), `*`(y[1])), `-`(`*`(`...
[`+`(`*`(`/`(484, 3), `*`(y[2])), `-`(`*`(`/`(484, 3), `*`(y[1]))), `-`(`*`(`^`(phi, 2), `*`(y[1])))), `+`(`*`(`/`(605, 4), `*`(y[3])), `-`(`*`(242, `*`(y[2]))), `*`(`/`(363, 4), `*`(y[1])), `-`(`*`(`...
(18)
 

> vars:=[seq(y[i],i=1..N)];
 

[y[1], y[2], y[3], y[4], y[5], y[6], y[7], y[8], y[9], y[10]] (19)
 

> A:=genmatrix(eqs,vars,'B1');
 

Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
(20)
 

> evalm(B1);
 

Typesetting:-mfenced(Typesetting:-mtable(Typesetting:-mtr(Typesetting:-mtd(Typesetting:-mn( (21)
 

Maple generates a row vector, which can be converted to a column vector as: 

> B:=matrix(N,1):for i to N do B[i,1]:=B1[i]:od:evalm(B);
 

Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mtable(Typesetting:-mtr(Typesetting:-mtd(Typesetting:-mn( (22)
 

The solution is obtained as 

> X:=evalm(inverse(A)&*B);
 

Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
Typesetting:-mrow(Typesetting:-mverbatim(
(23)
 

> for i to N do y[i]:=X[i,1];od;
 

 

 

 

 

 

 

 

 

 

`+`(`/`(`*`(6525466398347402995646847690), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504367867287826497, `*`(`^`(phi, 4))), `*`(1732908160...
`+`(`/`(`*`(6525466398347402995646847690), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504367867287826497, `*`(`^`(phi, 4))), `*`(1732908160...
`+`(`/`(`*`(6525466398347402995646847690), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504367867287826497, `*`(`^`(phi, 4))), `*`(1732908160...
`+`(`/`(`*`(6525466398347402995646847690), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504367867287826497, `*`(`^`(phi, 4))), `*`(1732908160...
`+`(`/`(`*`(`/`(26964737183253731386970445, 2), `*`(`+`(`*`(3, `*`(`^`(phi, 2))), 484))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504367...
`+`(`/`(`*`(`/`(26964737183253731386970445, 2), `*`(`+`(`*`(3, `*`(`^`(phi, 2))), 484))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504367...
`+`(`/`(`*`(`/`(26964737183253731386970445, 2), `*`(`+`(`*`(3, `*`(`^`(phi, 2))), 484))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504367...
`+`(`/`(`*`(`/`(26964737183253731386970445, 2), `*`(`+`(`*`(3, `*`(`^`(phi, 2))), 484))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504367...
`+`(`/`(`*`(`/`(26964737183253731386970445, 2), `*`(`+`(`*`(3, `*`(`^`(phi, 2))), 484))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504367...
`+`(`/`(`*`(89139627052078450866018, `*`(`+`(`*`(1210, `*`(`^`(phi, 2))), `*`(3, `*`(`^`(phi, 4))), 73205))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))),...
`+`(`/`(`*`(89139627052078450866018, `*`(`+`(`*`(1210, `*`(`^`(phi, 2))), `*`(3, `*`(`^`(phi, 4))), 73205))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))),...
`+`(`/`(`*`(89139627052078450866018, `*`(`+`(`*`(1210, `*`(`^`(phi, 2))), `*`(3, `*`(`^`(phi, 4))), 73205))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))),...
`+`(`/`(`*`(89139627052078450866018, `*`(`+`(`*`(1210, `*`(`^`(phi, 2))), `*`(3, `*`(`^`(phi, 4))), 73205))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))),...
`+`(`/`(`*`(89139627052078450866018, `*`(`+`(`*`(1210, `*`(`^`(phi, 2))), `*`(3, `*`(`^`(phi, 4))), 73205))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))),...
`+`(`/`(`*`(`/`(52620795190128955647, 2), `*`(`+`(`*`(7686525, `*`(`^`(phi, 2))), `*`(46464, `*`(`^`(phi, 4))), `*`(72, `*`(`^`(phi, 6))), 248018540))), `*`(`+`(6525466398347402995646847690, `*`(48806...
`+`(`/`(`*`(`/`(52620795190128955647, 2), `*`(`+`(`*`(7686525, `*`(`^`(phi, 2))), `*`(46464, `*`(`^`(phi, 4))), `*`(72, `*`(`^`(phi, 6))), 248018540))), `*`(`+`(6525466398347402995646847690, `*`(48806...
`+`(`/`(`*`(`/`(52620795190128955647, 2), `*`(`+`(`*`(7686525, `*`(`^`(phi, 2))), `*`(46464, `*`(`^`(phi, 4))), `*`(72, `*`(`^`(phi, 6))), 248018540))), `*`(`+`(6525466398347402995646847690, `*`(48806...
`+`(`/`(`*`(`/`(52620795190128955647, 2), `*`(`+`(`*`(7686525, `*`(`^`(phi, 2))), `*`(46464, `*`(`^`(phi, 4))), `*`(72, `*`(`^`(phi, 6))), 248018540))), `*`(`+`(6525466398347402995646847690, `*`(48806...
`+`(`/`(`*`(`/`(52620795190128955647, 2), `*`(`+`(`*`(7686525, `*`(`^`(phi, 2))), `*`(46464, `*`(`^`(phi, 4))), `*`(72, `*`(`^`(phi, 6))), 248018540))), `*`(`+`(6525466398347402995646847690, `*`(48806...
`+`(`/`(`*`(289921736584732538, `*`(`+`(`*`(1116083430, `*`(`^`(phi, 2))), `*`(11903133, `*`(`^`(phi, 4))), `*`(42592, `*`(`^`(phi, 6))), `*`(48, `*`(`^`(phi, 8))), 22507682505))), `*`(`+`(65254663983...
`+`(`/`(`*`(289921736584732538, `*`(`+`(`*`(1116083430, `*`(`^`(phi, 2))), `*`(11903133, `*`(`^`(phi, 4))), `*`(42592, `*`(`^`(phi, 6))), `*`(48, `*`(`^`(phi, 8))), 22507682505))), `*`(`+`(65254663983...
`+`(`/`(`*`(289921736584732538, `*`(`+`(`*`(1116083430, `*`(`^`(phi, 2))), `*`(11903133, `*`(`^`(phi, 4))), `*`(42592, `*`(`^`(phi, 6))), `*`(48, `*`(`^`(phi, 8))), 22507682505))), `*`(`+`(65254663983...
`+`(`/`(`*`(289921736584732538, `*`(`+`(`*`(1116083430, `*`(`^`(phi, 2))), `*`(11903133, `*`(`^`(phi, 4))), `*`(42592, `*`(`^`(phi, 6))), `*`(48, `*`(`^`(phi, 8))), 22507682505))), `*`(`+`(65254663983...
`+`(`/`(`*`(289921736584732538, `*`(`+`(`*`(1116083430, `*`(`^`(phi, 2))), `*`(11903133, `*`(`^`(phi, 4))), `*`(42592, `*`(`^`(phi, 6))), `*`(48, `*`(`^`(phi, 8))), 22507682505))), `*`(`+`(65254663983...
`+`(`/`(`*`(`/`(108911245899599, 2), `*`(`+`(`*`(8665457764425, `*`(`^`(phi, 2))), `*`(141498120192, `*`(`^`(phi, 4))), `*`(859953776, `*`(`^`(phi, 6))), `*`(2168320, `*`(`^`(phi, 8))), `*`(1920, `*`(...
`+`(`/`(`*`(`/`(108911245899599, 2), `*`(`+`(`*`(8665457764425, `*`(`^`(phi, 2))), `*`(141498120192, `*`(`^`(phi, 4))), `*`(859953776, `*`(`^`(phi, 6))), `*`(2168320, `*`(`^`(phi, 8))), `*`(1920, `*`(...
`+`(`/`(`*`(`/`(108911245899599, 2), `*`(`+`(`*`(8665457764425, `*`(`^`(phi, 2))), `*`(141498120192, `*`(`^`(phi, 4))), `*`(859953776, `*`(`^`(phi, 6))), `*`(2168320, `*`(`^`(phi, 8))), `*`(1920, `*`(...
`+`(`/`(`*`(`/`(108911245899599, 2), `*`(`+`(`*`(8665457764425, `*`(`^`(phi, 2))), `*`(141498120192, `*`(`^`(phi, 4))), `*`(859953776, `*`(`^`(phi, 6))), `*`(2168320, `*`(`^`(phi, 8))), `*`(1920, `*`(...
`+`(`/`(`*`(`/`(108911245899599, 2), `*`(`+`(`*`(8665457764425, `*`(`^`(phi, 2))), `*`(141498120192, `*`(`^`(phi, 4))), `*`(859953776, `*`(`^`(phi, 6))), `*`(2168320, `*`(`^`(phi, 8))), `*`(1920, `*`(...
`+`(`/`(`*`(138475837126, `*`(`+`(`*`(4673405164608180, `*`(`^`(phi, 2))), `*`(107636882352054, `*`(`^`(phi, 4))), `*`(973366475840, `*`(`^`(phi, 6))), `*`(4069026720, `*`(`^`(phi, 8))), `*`(7898880, ...
`+`(`/`(`*`(138475837126, `*`(`+`(`*`(4673405164608180, `*`(`^`(phi, 2))), `*`(107636882352054, `*`(`^`(phi, 4))), `*`(973366475840, `*`(`^`(phi, 6))), `*`(4069026720, `*`(`^`(phi, 8))), `*`(7898880, ...
`+`(`/`(`*`(138475837126, `*`(`+`(`*`(4673405164608180, `*`(`^`(phi, 2))), `*`(107636882352054, `*`(`^`(phi, 4))), `*`(973366475840, `*`(`^`(phi, 6))), `*`(4069026720, `*`(`^`(phi, 8))), `*`(7898880, ...
`+`(`/`(`*`(138475837126, `*`(`+`(`*`(4673405164608180, `*`(`^`(phi, 2))), `*`(107636882352054, `*`(`^`(phi, 4))), `*`(973366475840, `*`(`^`(phi, 6))), `*`(4069026720, `*`(`^`(phi, 8))), `*`(7898880, ...
`+`(`/`(`*`(138475837126, `*`(`+`(`*`(4673405164608180, `*`(`^`(phi, 2))), `*`(107636882352054, `*`(`^`(phi, 4))), `*`(973366475840, `*`(`^`(phi, 6))), `*`(4069026720, `*`(`^`(phi, 8))), `*`(7898880, ...
`+`(`/`(`*`(138475837126, `*`(`+`(`*`(4673405164608180, `*`(`^`(phi, 2))), `*`(107636882352054, `*`(`^`(phi, 4))), `*`(973366475840, `*`(`^`(phi, 6))), `*`(4069026720, `*`(`^`(phi, 8))), `*`(7898880, ...
`+`(`/`(`*`(`/`(572214203, 2), `*`(`+`(22807775005009454460, `*`(2968780630817346345, `*`(`^`(phi, 2))), `*`(91352854441102848, `*`(`^`(phi, 4))), `*`(1139394621712160, `*`(`^`(phi, 6))), `*`(69524557...
`+`(`/`(`*`(`/`(572214203, 2), `*`(`+`(22807775005009454460, `*`(2968780630817346345, `*`(`^`(phi, 2))), `*`(91352854441102848, `*`(`^`(phi, 4))), `*`(1139394621712160, `*`(`^`(phi, 6))), `*`(69524557...
`+`(`/`(`*`(`/`(572214203, 2), `*`(`+`(22807775005009454460, `*`(2968780630817346345, `*`(`^`(phi, 2))), `*`(91352854441102848, `*`(`^`(phi, 4))), `*`(1139394621712160, `*`(`^`(phi, 6))), `*`(69524557...
`+`(`/`(`*`(`/`(572214203, 2), `*`(`+`(22807775005009454460, `*`(2968780630817346345, `*`(`^`(phi, 2))), `*`(91352854441102848, `*`(`^`(phi, 4))), `*`(1139394621712160, `*`(`^`(phi, 6))), `*`(69524557...
`+`(`/`(`*`(`/`(572214203, 2), `*`(`+`(22807775005009454460, `*`(2968780630817346345, `*`(`^`(phi, 2))), `*`(91352854441102848, `*`(`^`(phi, 4))), `*`(1139394621712160, `*`(`^`(phi, 6))), `*`(69524557...
`+`(`/`(`*`(`/`(572214203, 2), `*`(`+`(22807775005009454460, `*`(2968780630817346345, `*`(`^`(phi, 2))), `*`(91352854441102848, `*`(`^`(phi, 4))), `*`(1139394621712160, `*`(`^`(phi, 6))), `*`(69524557...
`+`(`/`(`*`(556358, `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))), `*`(1039393...
`+`(`/`(`*`(556358, `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))), `*`(1039393...
`+`(`/`(`*`(556358, `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))), `*`(1039393...
`+`(`/`(`*`(556358, `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))), `*`(1039393...
`+`(`/`(`*`(556358, `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))), `*`(1039393...
`+`(`/`(`*`(556358, `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))), `*`(1039393...
`+`(`/`(`*`(`/`(121, 2), `*`(`+`(107858948733014925547881780, `*`(22062057695389416589339455, `*`(`^`(phi, 2))), `*`(1088875496968988624062464, `*`(`^`(phi, 4))), `*`(22558684271820716159536, `*`(`^`(...
`+`(`/`(`*`(`/`(121, 2), `*`(`+`(107858948733014925547881780, `*`(22062057695389416589339455, `*`(`^`(phi, 2))), `*`(1088875496968988624062464, `*`(`^`(phi, 4))), `*`(22558684271820716159536, `*`(`^`(...
`+`(`/`(`*`(`/`(121, 2), `*`(`+`(107858948733014925547881780, `*`(22062057695389416589339455, `*`(`^`(phi, 2))), `*`(1088875496968988624062464, `*`(`^`(phi, 4))), `*`(22558684271820716159536, `*`(`^`(...
`+`(`/`(`*`(`/`(121, 2), `*`(`+`(107858948733014925547881780, `*`(22062057695389416589339455, `*`(`^`(phi, 2))), `*`(1088875496968988624062464, `*`(`^`(phi, 4))), `*`(22558684271820716159536, `*`(`^`(...
`+`(`/`(`*`(`/`(121, 2), `*`(`+`(107858948733014925547881780, `*`(22062057695389416589339455, `*`(`^`(phi, 2))), `*`(1088875496968988624062464, `*`(`^`(phi, 4))), `*`(22558684271820716159536, `*`(`^`(...
`+`(`/`(`*`(`/`(121, 2), `*`(`+`(107858948733014925547881780, `*`(22062057695389416589339455, `*`(`^`(phi, 2))), `*`(1088875496968988624062464, `*`(`^`(phi, 4))), `*`(22558684271820716159536, `*`(`^`(...
`+`(`/`(`*`(`/`(121, 2), `*`(`+`(107858948733014925547881780, `*`(22062057695389416589339455, `*`(`^`(phi, 2))), `*`(1088875496968988624062464, `*`(`^`(phi, 4))), `*`(22558684271820716159536, `*`(`^`(...
(24)
 

> y[0]:=eval(y[0]);y[N+1]:=eval(y[N+1]);
 

 

`+`(`-`(`/`(`*`(`/`(8988245727751243795656815, 2), `*`(`+`(`*`(3, `*`(`^`(phi, 2))), 484))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504...
`+`(`-`(`/`(`*`(`/`(8988245727751243795656815, 2), `*`(`+`(`*`(3, `*`(`^`(phi, 2))), 484))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504...
`+`(`-`(`/`(`*`(`/`(8988245727751243795656815, 2), `*`(`+`(`*`(3, `*`(`^`(phi, 2))), 484))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504...
`+`(`-`(`/`(`*`(`/`(8988245727751243795656815, 2), `*`(`+`(`*`(3, `*`(`^`(phi, 2))), 484))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504...
`+`(`-`(`/`(`*`(`/`(8988245727751243795656815, 2), `*`(`+`(`*`(3, `*`(`^`(phi, 2))), 484))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504...
`+`(`-`(`/`(`*`(`/`(8988245727751243795656815, 2), `*`(`+`(`*`(3, `*`(`^`(phi, 2))), 484))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504...
`+`(`-`(`/`(`*`(`/`(8988245727751243795656815, 2), `*`(`+`(`*`(3, `*`(`^`(phi, 2))), 484))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504...
`+`(`-`(`/`(`*`(`/`(8988245727751243795656815, 2), `*`(`+`(`*`(3, `*`(`^`(phi, 2))), 484))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504...
`+`(`-`(`/`(`*`(`/`(8988245727751243795656815, 2), `*`(`+`(`*`(3, `*`(`^`(phi, 2))), 484))), `*`(`+`(6525466398347402995646847690, `*`(4880617430168925381041650545, `*`(`^`(phi, 2))), `*`(489700707504...
`+`(`-`(`/`(`*`(`/`(6119938, 35), `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))...
`+`(`-`(`/`(`*`(`/`(6119938, 35), `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))...
`+`(`-`(`/`(`*`(`/`(6119938, 35), `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))...
`+`(`-`(`/`(`*`(`/`(6119938, 35), `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))...
`+`(`-`(`/`(`*`(`/`(6119938, 35), `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))...
`+`(`-`(`/`(`*`(`/`(6119938, 35), `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))...
`+`(`-`(`/`(`*`(`/`(6119938, 35), `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))...
`+`(`-`(`/`(`*`(`/`(6119938, 35), `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))...
`+`(`-`(`/`(`*`(`/`(6119938, 35), `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))...
`+`(`-`(`/`(`*`(`/`(6119938, 35), `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))...
`+`(`-`(`/`(`*`(`/`(6119938, 35), `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))...
`+`(`-`(`/`(`*`(`/`(6119938, 35), `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))...
`+`(`-`(`/`(`*`(`/`(6119938, 35), `*`(`+`(11728898296326111956055, `*`(1938660875425803629100, `*`(`^`(phi, 2))), `*`(76666011704510603034, `*`(`^`(phi, 4))), `*`(1254579532990180672, `*`(`^`(phi, 6))...
(25)
 

Now the result obtained is plotted for different values of Thiele modulus Φ: 

> display({seq(p[i],i=1..5)});
 

Error, (in plots:-display) expecting plot structures but received: {p[2], p[4], p[5], p[3], p[1]}
 

> pars:=[0.1,0.5,1,2,5];
 

[.1, .5, 1, 2, 5] (26)
 

> clr:=[black,red,green,gold,blue];
 

[black, red, green, gold, blue] (27)
 

> for j from 1 to 5 do p[j]:=plot([seq([i*h,subs(phi=pars[j],y[i])],i=0..N+1)],thickness=4,title="Figure Exp 3.1.14.",axes=boxed,color=clr[j]):od:
 

> display({seq(p[i],i=1..5)});
 

Plot_2d
 

>