Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Scott J. McCaughrin Posts: 10 Registered: 12/12/04
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) 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

Date Subject Author
6/15/96 Scott J. McCaughrin
6/16/96 Bill Long