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Stability and Convergence Analysis of ERKN Integrators for Second-Order ODEs with Highly Oscillatory Solutions

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, we commence the nonlinear stability and convergence analysis of ERKN integrators for second-order ODEs with highly oscillatory solutions, depending on a frequency matrix. As one of the most important applications, we also rigorously analyse the global errors of the blend of the ERKN time integrators and the Fourier pseudospectral spatial discretisation (ERKN-FP) when applied to semilinear wave equations. The theoretical results show that the nonlinear stability and the global error bounds are entirely independent of the frequency matrix, and the spatial mesh size. The analysis also provides a new perspective on the class of ERKN time integrators. That is, the ERKN-FP methods are free from the restriction on the Courant-Friedrichs-Lewy (CFL) condition.

Suggested Citation

  • Xinyuan Wu & Bin Wang, 2021. "Stability and Convergence Analysis of ERKN Integrators for Second-Order ODEs with Highly Oscillatory Solutions," Springer Books, in: Geometric Integrators for Differential Equations with Highly Oscillatory Solutions, chapter 0, pages 75-122, Springer.
    • Handle: RePEc:spr:sprchp:978-981-16-0147-7_3
    DOI: 10.1007/978-981-16-0147-7_3
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