Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

Computation of integrals with oscillatory and singular integrandsHTML articles powered by AMS MathViewer

by Bing Yuan Ting and Yudell L. Luke
Math. Comp. 37 (1981), 169-183 Request permission

Abstract:

This paper is concerned with evaluation of integrals whose integrands are oscillatory and contain singularities at the endpoints of the interval of integration. A typical form is $G(\theta ) = \smallint _a^bw(x){e^{i\theta x}}f(x) dx$, where a and b can be finite or infinite, $\theta$ is a parameter which is usually large, $f(x)$ is analytic in the range of integration, and the singularities are encompassed in the weight function $w(x)$. We suppose that $f(x)$ can be expanded in series of polynomials which are orthogonal over the interval of integration with respect to $w(x)$. There are two such expansions for $f(x)$. One is an infinite series which follows from the usual orthogonality property. The other is a polynomial approximation plus a remainder. The relations between the coefficients in these representations are detailed and methods for the evaluation of these are analyzed. Error analyses are provided. A numerical example is given to illustrate the effectiveness of the schemes developed.
References
Similar Articles
• Retrieve articles in Mathematics of Computation with MSC: 65D30, 41A60
• Retrieve articles in all journals with MSC: 65D30, 41A60