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: ***