1lc.mac is from the book "Perturbation Methods, Bifurcation Theory and
2Computer Algebra" by Rand & Armbruster (Springer 1987)
3
4It uses Lindstedt's method to calculate limit cycles.
5
6maxima-5.9.0 cvs reproduces the results from the book.  The routine is
7case sensitive, and failed when the data was entered in lower case.
8
9The first example is from p6.  The differential equation is van der Pol's
10equation
11
12    w^2 x'' + x + e (x^2-1) w x' = 0
13
14(C1) load("lc.mac");
15(D1)                                lc.mac
16(C2) lc();
17THE D.E. IS OF THE FORM:  X'' + X + E * F(X,X') = 0
18ENTER F(X,Y), REPRESENTING X' AS Y
19Y*(X^2-1);
20                             2
21THE D.E. IS: X'' + X + E ( (X  - 1) Y ) = 0
22ENTER TRUNCATION ORDER
234;
24CHOICES FOR LIMIT CYCLE AMPLITUDE:
251 )   - 2
262 )   2
273 )   0
28ENTER CHOICE NUMBER
292;
30DONE WITH STEP 1 OF 4
31DONE WITH STEP 2 OF 4
32DONE WITH STEP 3 OF 4
33DONE WITH STEP 4 OF 4
34               (SIN(3 Z) - 3 SIN(Z)) E
35X = 2 COS(Z) - -----------------------
36                          4
37
38                                           2
39   (5 COS(5 Z) - 18 COS(3 Z) + 12 COS(Z)) E
40 - -----------------------------------------
41                      96
42
43                                                            3
44   (28 SIN(7 Z) - 140 SIN(5 Z) + 189 SIN(3 Z) - 63 SIN(Z)) E
45 + ---------------------------------------------------------- + . . .
46                              2304
47        4    2
48    17 E    E
49W = ----- - -- + 1
50    3072    16
51                                    4    2
52                                17 E    E
53(D2)                            ----- - -- + 1
54                                3072    16
55
56
57Local Variables: ***
58mode: Text ***
59End: ***