share/contrib/rand/Oden.bk1

   1 /* Filename <name>.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 (d4) This program generates the Taylor series solution
  15
  16
  17 to the Nth order ODE:
  18
  19
  20             (N)                             (N-1)
  21
  22
  23            Y    =  F ( X, Y, Y', Y'', ..., Y      )
  24
  25
  26 for arbitrary initial conditions at X = 0.
  27
  28
  29 To call it, type:
  30
  31
  32                    SOLUTION()
  33
  34 */
  35
  36 \rsolution():=(input(),step1(),step2(),v:f,
  37          for i from n thru m do (u:u+evaluate(v)*x^i/i!,v:deriv(v)),output())$
  38 input():=(n:read("ENTER ORDER OF D.E."),m:read("ENTER DEGREE OF TRUNCATION"),
  39       f:read("ENTER RIGHT HAND SIDE OF ODE.\
  40 REPRESENT Y BY Y[0], Y' BY Y[1], ETC."),
  41       print(" "),print(f),print(" "),
  42       for i from 0 thru n-1 do z[i]:read("ENTER INITIAL VALUE OF Y[",i,"]"))$
  43 step1():=u:sum(z[i]*x^i/i!,i,0,n-1)$
  44 step2():=initial:makelist([y[i] = z[i]],i,0,n-1)$
  45 deriv(g):=diff(g,x)+sum(diff(g,y[i])*y[i+1],i,0,n-2)+diff(g,y[n-1])*f$
  46 evaluate(g):=ev(g,x:0,initial)$
  47 output():=print("Y =",u)$