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

共 50 条

[1] Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space distributed-order diffusion equation
Zhao, Jingjun
Zhang, Yanming
Xu, Yang
[J]. APPLIED NUMERICAL MATHEMATICS, 2020, 157 : 223 - 235
[2] Implicit Runge-Kutta and spectral Galerkin methods for Riesz space fractional/distributed-order diffusion equation
Zhao, Jingjun
Zhang, Yanming
Xu, Yang
[J]. COMPUTATIONAL & APPLIED MATHEMATICS, 2020, 39 (02):
[3] Implicit Runge-Kutta with spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian
Zhang, Yanming
Li, Yu
Yu, Yuexin
Wang, Wansheng
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2024, 40 (03)
[4] Implicit Runge–Kutta and spectral Galerkin methods for Riesz space fractional/distributed-order diffusion equation
Jingjun Zhao
Yanming Zhang
Yang Xu
[J]. Computational and Applied Mathematics, 2020, 39
[5] A Note on Stability Analysis of Two-Dimensional Runge-Kutta Discontinuous Galerkin Methods
Xu, Yuan
Zhang, Qiang
[J]. COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, 2024,
[6] Fast TTTS iteration methods for implicit Runge-Kutta temporal discretization of Riesz space fractional advection-diffusion equations ?
She, Zi-Hang
Qiu, Li-Min
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2023, 141 : 42 - 53
[7] A Runge-Kutta Gegenbauer spectral method for nonlinear fractional differential equations with Riesz fractional derivatives
Lin, Fu-Rong
Qu, Haidong
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2019, 96 (02) : 417 - 435
[8] Numerical solution for multi-dimensional Riesz fractional nonlinear reaction-diffusion equation by exponential Runge-Kutta method
Zhang, Lu
Sun, Hai-Wei
[J]. JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2020, 62 (1-2) : 449 - 472
[9] General linear and spectral Galerkin methods for the Riesz space fractional diffusion equation
Xu, Yang
Zhang, Yanming
Zhao, Jingjun
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2020, 364
[10] High-Order Accurate Runge-Kutta (Local) Discontinuous Galerkin Methods for One- and Two-Dimensional Fractional Diffusion Equations
Ji, Xia
Tang, Huazhong
[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2012, 5 (03) : 333 - 358

← 1 2 3 4 5 →