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Re: numerical integration problem

• To: mathgroup at smc.vnet.net
• Subject: [mg77868] Re: numerical integration problem
• From: dh <dh at metrohm.ch>
• Date: Mon, 18 Jun 2007 07:09:09 -0400 (EDT)
• References: <f532hu$36j$1@smc.vnet.net>

Hi Sean,

you could e.g. numerically approximate your function x[w] using 

FunctionInterpolation or even Interpolation. Afterwards, the integration 

should be easy.

hope this helps, Daniel



Sean wrote:

> 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

>