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

被引：6

作者：

Zhao, Jingjun ^{[1
]}

Zhang, Yanming ^{[2
]}

Xu, Yang ^{[2
]}

机构：

[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

[2] Harbin Inst Technol, Sch Math, Harbin 150001, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2020年 / 386卷

基金：

中国国家自然科学基金;

关键词：

Nonlinear Riesz space fractional equation; Implicit Runge-Kutta method; Spectral Galerkin method; Convergence; Stability; COMPACT ADI SCHEME; ANOMALOUS DIFFUSION; COLLOCATION METHOD; DIFFERENCE SCHEME; APPROXIMATION; 4TH-ORDER; EFFICIENT;

D O I：

10.1016/j.amc.2020.125505

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A numerical method with high accuracy both in time and in space is proposed for the two-dimensional nonlinear Riesz space fractional diffusion equation. The main idea is based on a spectral Galerkin method in spatial direction and an s-stage implicit Runge-Kutta method in temporal direction. A rigorous stability and error analysis is performed for the proposed method. It is shown that the proposed method is stable and convergent. The optimal spa-tial error estimate is also derived. Numerical experiments are provided to illustrate the theoretical results. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：15

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