NUMERICAL INTEGRATION OF OSCILLATING FUNCTIONS HAVING A NON-LINEAR ARGUMENT,
Abstract
A procedure is described for numerical evaluation of integrals of the type 'integral -nh to nh of f(x) sin g(x) cos g(x) dx'. Both f(x) and g(x) may be arbitrary functions having no restrictions except that they be sufficiently differentiable and single-valued. The method, which is a generalization of Filon's quadrature formula, is most useful when g(x) is a rapidly varying, nonlinear quantity. Three- and five-point formulas are presented. The essential feature of the method is replacement of the nonlinear function g(x) by a linear function plus an increment delta(x). If step lengths in the x-direction are so chosen that delta does not vary greatly over the interval of integration, then sin delta or cos delta can be approximated satisfactorily by a low-order polynomial, and quadrature of Filon's type can be performed. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 20, 1967
- Accession Number
- AD0648817
Entities
People
- A. M. O. Smith
Organizations
- Douglas