Accession Number : AD0648817

Title :   NUMERICAL INTEGRATION OF OSCILLATING FUNCTIONS HAVING A NON-LINEAR ARGUMENT,

Corporate Author : DOUGLAS AIRCRAFT CO INC LONG BEACH CALIF AIRCRAFT DIV

Personal Author(s) : Smith,A. M. O.

Report Date : 20 FEB 1967

Pagination or Media Count : 13

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)

Descriptors :   (*FUNCTIONS(MATHEMATICS), *NUMERICAL INTEGRATION), NUMERICAL ANALYSIS, OSCILLATION, NONLINEAR SYSTEMS, INTEGRALS

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE