A space‐time spectral collocation method for the 2‐dimensional nonlinear Riesz space fractional diffusion equations

Abstract

The space-time spectral collocation method was initially presented for the 1-dimensional sine-Gordon equation. In this article, we introduce a space-time spectral collocation method for solving the 2-dimensional nonlinear Riesz space fractional diffusion equations. The method is based on a Legendre-Gauss-Lobatto spectral collocation method for discretizing spatial and the spectral collocation method for the time nonlinear first-order system of ordinary differential equation. Optimal priori error estimates in L 2 norms for the semidiscrete formulation and the uniqueness of the approximate solution are derived. The method has spectral accuracy in both space and time, and the numerical results confirm the statement. KEYWORDSerror estimates, nonlinear initial-value problems, Riesz fractional derivative, space-time spectral method, spectral collocation method 6130

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