Name:    Double Integration
Models:  fx-4000P and above
Size:    361 bytes
Version: 1.1
Author:  Lupus Yonderboy
E-mail:  lupusy@afrodita.rcub.bg.ac.yu
URL:     http://www.rcub.bg.ac.yu/~lupusy/

Description:
   'Double' integral solver.  Will solve integrals of the form:

       d  b
       / /
       | | f(x,y) dxdy
       / /
      c a

   This  is  NOT  my program, I don't even understand it completely...  I
   just  modified  an  ancient  ZX Spectrum listing :) but it works fine,
   although  it can be slow.  Calculations can take 5 sec up to few years
   :) , depending on M and N values.

   Complete  formula  is  too  large,  this  is only the part used in the
   program:

   Xi=a+ih, i=0,1,...,n;  (X0=a, Xn=b);  h=(b-a)/n
   Yj=c+jk, j=0,1,...,m;  (Y0=c, Yn=d);  k=(d-c)/m


Usage:
   Nothing  tricky there, program will ask you to enter a, b, c, d limits
   and  m  and  n  coeffs.   Than  you  need  to  arm  yourself with some
   patience :)
   There  is  one  important  thing:  when  you  are  dealing  with trig.
   functions (as in example below), you need to put calc in 'Rad' mode.

Example:

   pi pi
    / /
    | | abs (cos(x+y)) dxdy  =  2pi  (approx. 6.283185307)
    / /
   0 0

   (put calc in 'Rad' mode)

   m= 5, n= 5,  calc. time = 0m  4.5s,  Ans = 6.143752112
   m=15, n=15,  calc. time = 0m 35.0s,  Ans = 5.823672472
   m=20, n=20,  calc. time = 1m  2.0s,  Ans = 5.88064076
   m=25, n=25,  calc. time = 1m 59.0s,  Ans = 5.958442107
   m=50, n=50,  calc. time = 6m 35.0s,  Ans = 6.099883503

   This  shows  that  m=n=5  gives  best  time/value  results,  but still
   inaccurate...   Anyway,  this  program is intended for quick-checking,
   and  if  you  use it at exam, put m=n=70 and it might finish just when
   you finish your calculations ;)