share/contrib/rand/duffing.mac

   1 /* Filename duffing.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
  16 (d4) This program computes a perturbation solution for
  17
  18
  19 the periodic response of Duffing's equation.
  20
  21
  22 Call it by typing:
  23
  24
  25                      DUFFING(N)
  26
  27
  28 where N is the order of truncation.
  29 */
  30
  31 duffing(n):=(setup1(n),setup2(n),
  32         for i thru n do
  33             (step1(i),step2(i),step3(i),step4(i),step5(i),output1(i)),
  34         output2(n))$
  35 setup1(n):=(w:1,for i thru n do w:w+k[i]*e^i,x:a*cos(t),
  36        for i thru n do x:x+y[i](t)*e^i)$
  37 setup2(n):=(temp1:diff(x,t,2)+x/w^2+e*x^3/w^2-e*f*cos(t)/w^2,
  38        temp1:taylor(temp1,e,0,n),for i thru n do eq[i]:coeff(temp1,e,i))$
  39 step1(i):=temp1
  40       :expand(trigreduce(expand(ev(eq[i],makelist([e[j],f[j]],j,1,i-1),
  41                                    diff))))$
  42 step2(i):=(f[i]:solve(coeff(temp1,cos(t)),k[i]),temp1:ev(temp1,f[i]))$
  43 step3(i):=(temp1:ode2(temp1,y[i](t),t),
  44   temp1:subst(a[i],%k1,temp1),temp1:subst(b[i],%k2,temp1))$
  45 step4(i):=(temp2:rhs(temp1),temp2:diff(temp2,t),
  46       temp2:solve([ev(rhs(temp1),t:0),ev(temp2,t:0)],[a[i],b[i]]))$
  47 step5(i):=e[i]:ev(temp1,temp2)$
  48 output1(i):=(print(expand(e[i])),print(" "))$
  49 output2(n):=(print("w=",ev(w,makelist([f[j]],j,1,n))),print(" "))$