Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:313

Article

Wang, Bin¹  Wu, Xinyuan²  Meng, Fanwei¹ 

[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

[2] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

关键词: Trigonometric collocation methods;    Lagrange polynomials;    Multi-frequency oscillatory second-order systems;    Variation-of-constants formula;   

DOI  :  10.1016/j.cam.2016.09.017

来源: Elsevier

【 摘 要 】

In the present work, a kind of trigonometric collocation methods based on Lagrange basis polynomials is developed for effectively solving multi-frequency oscillatory second-order differential equations q '' (t) + Mq(t) = f (q(t)). The properties of the obtained methods are investigated. It is shown that the convergent condition of these methods is independent of parallel to M parallel to. which is very crucial for solving oscillatory systems. A fourth-order scheme of the methods is presented. Numerical experiments are implemented to show the remarkable efficiency of the methods proposed in this paper. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

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