Accession Number:

AD0648817

Title:

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

Descriptive Note:

Corporate Author:

DOUGLAS AIRCRAFT CO INC LONG BEACH CALIF AIRCRAFT DIV

Personal Author(s):

Report Date:

1967-02-20

Pagination or Media Count:

13.0

Abstract:

A procedure is described for numerical evaluation of integrals of the type integral -nh to nh of fx sin gx cos gx dx. Both fx and gx may be arbitrary functions having no restrictions except that they be sufficiently differentiable and single-valued. The method, which is a generalization of Filons quadrature formula, is most useful when gx 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 gx by a linear function plus an increment deltax. 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 Filons type can be performed. Author

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE