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 involves a linear system with a constant coefficient matrix. Taking the nonlinear Klein-Gordon equation and the nonlinear Schrödinger equation for examples, we derive the concrete energy-preserving schemes and demonstrate their high efficiency through numerical experiments.