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

This paper constructs two efficient exponential energy-preserving schemes for solving the fractional Klein-Gordon Schrodinger 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 Schrodinger equations, it is demonstrated that the proposed schemes are efficient, conserve energy, and have better numerical stability results than traditional schemes.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

This paper constructs two efficient exponential energy-preserving schemes for solving the fractional Klein-Gordon Schrodinger equation, which are built upon the newly proposed partitioned averaged vector field method and exponential time difference technique. The schemes also apply the Fourier pseudo-spectral method to discretize the fractional Laplacian operator and utilize the FFT technique to reduce computational complexity. Numerical experiments demonstrate that the proposed schemes are efficient, conserve energy, and exhibit better numerical stability results compared to traditional schemes.