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numerical integration problem

• To: mathgroup at smc.vnet.net
• Subject: [mg77818] numerical integration problem
• From: Sean <sshiau2 at wisc.edu>
• Date: Sun, 17 Jun 2007 06:12:04 -0400 (EDT)

Hi, 
  I know that to post a technical question here, it is best to give an example.
  But my program is huge but straightforward, so I hope to make clear my problem by simply describing how I design the program.

  My problem at hand is that I have a list of linearly coupled equations whose coefficients are normal functions of some parameters. 
  for a simple example

   x*f[w]+y*g[w]=z[w];
  x*b[w]+y*m[w]=n[w];

 I need to solve for x and y. Of course, the naive way is to put these equations into a matrix and solve for x and y----remember my problem has a 20 X 20 matrix. After this, x and y are expressed in terms of these functions. I just defind them as

x[w_]:=...;
y[w_]:=...;
Now I need to do a numerical integration over these functions x[w], and y[w].. But the trouble comes. Because of these huge expressions for the target functions x[w] and y[w], my dram is immediately eaten up and mathematica automatically terminates the program...
I read in a previous post 
that suggests if I redefine 
x[w_?NumerQ];= ... ;
y[w_?NumerQ]:=...;

Would this help, or there is a smarter way of fomulating my problem so that it would run faster and use less memory.

Your help is greatly appreciated,

Sean