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Exponential Collocation Methods for Conservative or Dissipative Systems

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

The main purpose of this chapter is to present exponential collocation methods (ECMs) for solving conservative or dissipative systems. ECMs can be of arbitrarily high order and preserve exactly or approximately first integrals or Lyapunov functions. In particular, the application of ECMs to stiff gradient systems is discussed in detail, and it turns out that ECMs are unconditionally energy-diminishing and strongly damped even for very stiff gradient systems. As a consequence of this discussion, arbitrary-order trigonometric/RKN collocation methods are also presented and analysed for second-order highly oscillatory/general systems. The chapter is accompanied by numerical results that demonstrate the potential value of this research.

Suggested Citation

  • Xinyuan Wu & Bin Wang, 2021. "Exponential Collocation Methods for Conservative or Dissipative Systems," Springer Books, in: Geometric Integrators for Differential Equations with Highly Oscillatory Solutions, chapter 0, pages 147-177, Springer.
    • Handle: RePEc:spr:sprchp:978-981-16-0147-7_5
    DOI: 10.1007/978-981-16-0147-7_5
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