English

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

Numerical Analysis 2018-02-22 v1

Abstract

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))q^{\prime\prime}(t)+Mq(t)=f\big(q(t)\big). The properties of the obtained methods are investigated. It is shown that the convergent condition of these methods is independent of \normM\norm{M}, 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.

Keywords

Cite

@article{arxiv.1608.06531,
  title  = {Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations},
  author = {Bin Wang and Xinyuan Wu and Fanwei Meng},
  journal= {arXiv preprint arXiv:1608.06531},
  year   = {2018}
}
R2 v1 2026-06-22T15:28:04.091Z