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

In: Geometric Integrators for Differential Equations with Highly Oscillatory Solutions

Author

Listed:
  • Xinyuan Wu

    (Nanjing University, Department of Mathematics)

  • Bin Wang

    (Xi’an Jiaotong University, School of Mathematics and Statistics)

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.

Suggested Citation

  • Xinyuan Wu & Bin Wang, 2021. "Oscillation-Preserving Integrators for Highly Oscillatory Systems of Second-Order ODEs," Springer Books, in: Geometric Integrators for Differential Equations with Highly Oscillatory Solutions, chapter 0, pages 1-45, Springer.
    • Handle: RePEc:spr:sprchp:978-981-16-0147-7_1
    DOI: 10.1007/978-981-16-0147-7_1
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