Two-frequency-dependent Gauss quadrature rules

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:174

Article

Kim, KJ

关键词: quadrature rule;    oscillatory integrand;    integration formula;   

DOI  :  10.1016/j.cam.2004.03.020

来源: Elsevier

【 摘 要 】

We construct two-frequency-dependent Gauss quadrature rules which can be applied for approximating the integration of the product of two oscillatory functions with different frequencies beta(1) and beta(2) of the forms, y(i)(x) = f(i,1)(x) cos(beta(i)x) + f(1,2)(x) Sin (beta(i)x), i = 1, 2, where the functions f(i,j)(x) are smooth. A regularization procedure is presented to avoid the singularity of the Jacobian matrix of nonlinear system of equations which is induced as one frequency approaches the other frequency. We provide numerical results to compare the accuracy of the classical Gauss rule and one- and two-frequency-dependent rules. (C) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

Free