A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation

Abstract

In this paper, we generalize the exponential energy-preserving integrator proposed in the recent paper [SIAM J. Sci. Comput. 38(2016) A1876-A1895] for conservative systems, which now becomes linearly implicit by further utilizing the idea of the scalar auxiliary variable approach. Comparing with the original exponential energy-preserving integrator which usually leads to a nonlinear algebraic system, our new method only involve a linear system with constant coefficient matrix. Taking the nonlinear Klein-Gordon equation for example, we derive the concrete energy-preserving scheme and demonstrate its high efficiency through numerical experiments.

21 pages, 13 figures

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Cited by in corpus (4)

• Mass- and energy-preserving exponential Runge-Kutta methods for the nonlinear Schrödinger equation
• Efficient energy-preserving exponential integrators for multi-components Hamiltonian systems
• A new symmetric linearly implicit exponential integrator preserving polynomial invariants or Lyapunov functions for conservative or dissipative systems
• Optimal convergence and long-time conservation of exponential integration for Schrödinger equations in a normal or highly oscillatory regime