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Topic: Numerical integration of a parametric function
Replies: 2   Last Post: Jun 16, 1996 12:11 AM

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Scott J. McCaughrin

Posts: 10
Registered: 12/12/04
Re: Numerical integration of a parametric function
Posted: Jun 15, 1996 8:01 PM
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In a previous article, mkolios@oci.utoronto.ca (Michael Kolios) says:

>I would like to numerically integrate something that looks like:
>
>int( theta * cos(nr) * dr, r=0..1)
>
>where I know theta(x) and r(x) and thus theta as a function of r is
>given parametrically by the mentioned two functions.
>
>The problem is that the "n" in the cosine term of the integrand becomes
>very large in this finite interval and thus to evaluate this I use
>special fortran routines that handle oscillatory integrals (e.g. dqawoe
>from slatec). Invariably, all of these routines require I specify the
>function (theta) non-parametrically.


So don't use them. If nr > 2pi, then nr = Q*2pi + R, 0<=R<2pi, Q integer;
cos(nr) = cos(Q*2pi + R) = cos(Q*2pi)cos(R) - sin(Q2pi)sin(R)
= cos(R).
Find R = Remainder(nr,2pi)
and apply cosine to R.

Best Regards,
Scott







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