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Volume-Preserving Exponential Integrators

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

Since various dynamical systems preserve volume in phase space, such as all Hamiltonian systems, this qualitative geometrical property of the analytical solution should be preserved within the framework of Geometric Integration. This chapter considers the volume-preserving exponential integrators for different vector fields. We first analyse a necessary and sufficient condition of volume preservation for exponential integrators. We then discuss volume-preserving exponential integrators for four kinds of vector fields. It turns out that symplectic exponential integrators can be volume preserving for a much larger class of vector fields than Hamiltonian systems. On the basis of this profound analysis, the applications of volume-preserving exponential integrators are demonstrated. For solving highly oscillatory second-order systems, efficient volume-preserving exponential integrators are derived, and for separable partitioned systems, volume-preserving ERKN integrators are presented. Moreover, volume-preserving RKN methods are also investigated.

Suggested Citation

  • Xinyuan Wu & Bin Wang, 2021. "Volume-Preserving Exponential Integrators," Springer Books, in: Geometric Integrators for Differential Equations with Highly Oscillatory Solutions, chapter 0, pages 179-211, Springer.
    • Handle: RePEc:spr:sprchp:978-981-16-0147-7_6
    DOI: 10.1007/978-981-16-0147-7_6
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