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

Bin Wang; Xinyuan Wu; Fanwei Meng

doi:10.1016/j.cam.2016.09.017

paper

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

arXiv:1608.06531 · doi:10.1016/j.cam.2016.09.017

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 $q^{''} (t) + M q (t) = f (q (t))$ . The properties of the obtained methods are investigated. It is shown that the convergent condition of these methods is independent of $\norm{M}$, 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.