Fast evaluation for the two-dimensional nonlinear coupled time-space fractional Klein-Gordon-Zakharov equations

In this paper, we develop a fast algorithm to solve the two-dimensional nonlinear coupled time-space fractional Klein-Gordon-Zakharov (KGZ) equations. The L2 - 1(sigma) method based on an efficient sum-of-exponentials (SOE) approximation and a Fourier spectral method are used to approximate the time and space direction, respectively. And we use the previous time levels to deal with the nonlinear terms to obtain a linearized numerical scheme. Finally, a numerical example is given to show that our numerical method is of second order accuracy in time, spectral accuracy in space and the fast algorithm is effective. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper presents a fast algorithm to solve the two-dimensional nonlinear coupled time-space fractional Klein-Gordon-Zakharov (KGZ) equations, utilizing an efficient sum-of-exponentials (SOE) approximation and a Fourier spectral method to approximate the time and space directions, and leveraging previous time levels to handle nonlinear terms. A numerical example demonstrates that the numerical method achieves second order accuracy in time, spectral accuracy in space, and the fast algorithm is effective.