Asymptotic expansions for the Bessel transformations with high oscillations by using the homotopy technique

作者：Chen, Ruyun^*; Liang, Ximing

来源：International Journal of Computer Mathematics, 2011, 88(13): 2872-2887.

DOI：10.1080/00207160.2011.561837

• homotopy perturbation method
• asymptotic expansion
• the Bessel transformation
• oscillatory integrals
• numerical quadrature

In this paper, we establish the asymptotic expansions for the integration containing the Bessel functions with high oscillations by using the homotopy technique. The proposed method is constructed by approximating the non-oscillatory or low-oscillatory factor in practice. Two cases are considered, that is, the case 0 is not an element of [a, b] and the case 0 is an element of [a, b], where [a, b] denotes the integration interval. The efficiency of the technique and the correctness of the theory are shown by several

• 出版日期2011
• 单位广东海洋大学; 中南大学