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Re: Numerical integration of a parametric function
Posted:
Jun 15, 1996 8:01 PM


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) nonparametrically.
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



