
Accession Number : AD0648817
Title : NUMERICAL INTEGRATION OF OSCILLATING FUNCTIONS HAVING A NONLINEAR 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 singlevalued. 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 fivepoint 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 xdirection 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 loworder 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