Abstract
In this paper, we develop a fast algorithm to solve the two-dimensional nonlinear coupled time–space fractional Klein–Gordon–Zakharov (KGZ) equations. The L2−1σ 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.
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