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Oscillation-Preserving Integrators for Highly Oscillatory Systems of Second-Order ODEs

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Geometric Integrators for Differential Equations with Highly Oscillatory Solutions

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Abstract

In this chapter, from the point of view of Geometric Integration, i.e. the numerical solution of differential equations using integrators that preserve as many as possible the geometric/physical properties of them, we first introduce the concept of oscillation preservation for Runge–Kutta–Nyström (RKN)-type methods and then analyse the oscillation-preserving behaviour of RKN-type methods in detail. This chapter is also accompanied by numerical experiments which show the importance of the oscillation-preserving property for a numerical method, and the remarkable superiority of oscillation-preserving integrators for solving nonlinear multi-frequency highly oscillatory systems.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, Jiangsu, China

    Xinyuan Wu

  2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, China

    Bin Wang

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  1. Xinyuan Wu
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  2. Bin Wang
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Wu, X., Wang, B. (2021). Oscillation-Preserving Integrators for Highly Oscillatory Systems of Second-Order ODEs. In: Geometric Integrators for Differential Equations with Highly Oscillatory Solutions. Springer, Singapore. https://doi.org/10.1007/978-981-16-0147-7_1

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