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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
>
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