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Continuous-Stage Leap-Frog Schemes for Semilinear Hamiltonian Wave Equations

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 standard leap-frog scheme is a well-known time integration scheme for some nonlinear partial differential equations due to its simplicity and its ease of implementation. The main aim of this chapter is to present continuous-stage modified leap-frog schemes for high-dimensional semilinear Hamiltonian wave equations. We begin with the formulation of the wave equation as an abstract second-order ordinary differential equation (ODE) and its operator-variation-of-constants formula.

Suggested Citation

  • Xinyuan Wu & Bin Wang, 2021. "Continuous-Stage Leap-Frog Schemes for Semilinear Hamiltonian Wave Equations," Springer Books, in: Geometric Integrators for Differential Equations with Highly Oscillatory Solutions, chapter 0, pages 393-426, Springer.
    • Handle: RePEc:spr:sprchp:978-981-16-0147-7_12
    DOI: 10.1007/978-981-16-0147-7_12
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