A method to generate generalized quadrature rules foroscillatory integrals

✍ Scribed by K.C. Chung; G.A. Evans; J.R. Webster

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 70 KB
• Volume: 34
• Category: Article
• ISSN: 0168-9274
• DOI: 10.1016/s0168-9274(99)00033-1

✦ Synopsis

In a recent paper Evans and Webster produced a quadrature rule for oscillatory integrals with a trigonometric kernel. Their method is a modification of an earlier method due to Levin, and involves making a quadrature rule exact for a set of functions for which the modified moments have a simple closed form. In this paper we extend their method to deal with any oscillatory kernel, provided only that it satisfies a (known) linear ordinary differential equation. Some specific examples involving Bessel functions and Bessel-Trig combinations are given to illustrate the practical use of the method.