Two efficient exponential energy-preserving schemes for the fractional Klein–Gordon Schrödinger equation

Abstract

This paper constructs two efficient exponential energy-preserving schemes for solving the fractional Klein–Gordon Schrödinger equation. The developed schemes are built upon the newly proposed partitioned averaged vector field method and exponential time difference technique and enjoy some advantages of the partitioned averaged vector field method. In addition, the Fourier pseudo-spectral method is applied to discretize the fractional Laplacian operator to obtain schemes so that the FFT technique can be used to reduce the computational complexity of the developed schemes in long-time simulations. Finally, by solving some fractional Klein–Gordon Schrödinger equations, it is demonstrated that the proposed schemes are efficient, conserve energy, and have better numerical stability results than traditional schemes.