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arXiv · 1608.06531

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

Bin Wang·Xinyuan Wu·Fanwei Meng
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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 $q^{\prime\prime}(t)+Mq(t)=f\big(q(t)\big)$. The properties of the obtained methods are investigated. It is shown that the convergent condition of these methods is independent of $\norm{M}$, 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.

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Bin Wang, Xinyuan Wu, Fanwei Meng. 2016-08-23. Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations. https://doi.org/10.1016/j.cam.2016.09.017

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