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

Xinyuan Wu () and Bin Wang ()
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Xinyuan Wu: Nanjing University, Department of Mathematics
Bin Wang: Xi’an Jiaotong University, School of Mathematics and Statistics

Chapter Chapter 1 in Geometric Integrators for Differential Equations with Highly Oscillatory Solutions, 2021, pp 1-45 from Springer

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-16-0147-7_1

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DOI: 10.1007/978-981-16-0147-7_1

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