Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space fractional diffusion equation

作者：

Highlights：

• The proposed numerical method has high accuracy both in time and in space.

• Stability and convergence are analyzed in theory.

• The optimal spatial error estimate is provided.

摘要

•The proposed numerical method has high accuracy both in time and in space.•Stability and convergence are analyzed in theory.•The optimal spatial error estimate is provided.

论文关键词：Nonlinear Riesz space fractional equation,Implicit Runge-Kutta method,Spectral Galerkin method,Convergence,Stability

论文评审过程：Received 18 September 2019, Revised 30 April 2020, Accepted 28 June 2020, Available online 10 July 2020, Version of Record 10 July 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125505