1/* Filename mathieu0.mac
2
3   ***************************************************************
4   *							         *
5   *                     <package name>                          *
6   *                <functionality description>                  *
7   *                                                             *
8   *          from: Computer Algebra in Applied Math.            *
9   *                   by Rand (Pitman,1984)                     *
10   *                Programmed by Richard Rand                   *
11   *      These files are released to the public domain          *
12   *            						 *
13   ***************************************************************
14*/ /*
15(d4) This program computes the transition curve through
16
17
18the origin (N = 0) in Mathieu's equation using a perturbation
19
20
21method.  To call it, type
22
23
24                     MATHIEU0()
25
26*/
27
28mathieu0():=(input(),setup1(),setup2(),
29	 for i thru m do (step1(),step2a(),step3a()),output())$
30input():=m:read("ENTER DEGREE OF TRUNCATION")$
31setup1():=(w:0,for i thru m do w:w+k[i]*e^i,x:1,
32       for i thru m do x:x+y[i](t)*e^i)$
33setup2():=(temp1:diff(x,t,2)+x*(w+e*cos(t)),temp1:taylor(temp1,e,0,m),
34       for i thru m do eq[i]:coeff(temp1,e,i))$
35step1():=temp1
36      :expand(trigreduce(expand(ev(eq[i],makelist([e[j],f[j]],j,1,i-1),
37				   diff))))$
38step2a():=(temp1:ode2(temp1,y[i](t),t),temp1:ev(temp1,%k1:0,%k2:0))$
39step3a():=(f[i]:solve(coeff(expand(rhs(temp1)),t,2),k[i]),e[i]:ev(temp1,f[i]))$
40output():=(print("delta=",ev(w,makelist([f[j]],j,1,m))),print(" "))$
41