Numerical simulation for the two-dimensional and three-dimensional Riesz space fractional diffusion equations with delay and a nonlinear reaction term. Issue 10 (3rd October 2019)

• Record Type: Journal Article
• Authors: Yang, Shuiping
• Is Part Of: International journal of computer mathematics. Volume 96:Issue 10(2019)
• Page Start: 1957
• Page End: 1978
• Publication Date: 2019-10-03
• Subjects: Riesz space fractional diffusion equations with delay -- nonlinear reaction term -- alternating direction method -- richardson extrapolation method -- stability and convergence; 34K37 -- 35K58 -- 65M06 -- 65M12; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2018.1544366
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: In this research, we consider the alternating direction implicit method for solving the two-dimensional and three-dimensional Riesz space fractional diffusion equations with delay and a nonlinear reaction term. The corresponding theoretical results including stability and convergence are provided. Moreover, the convergence order of the proposed method is improved by using the Richardson extrapolation method. The numerical results are presented to show the robustness and effectiveness of the numerical method.