A fourth-order compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction–diffusion equation. Issue 9 (1st September 2020)

• Record Type: Journal Article
• Authors: Hu, Dongdong; Cao, Xuenian
• Is Part Of: International journal of computer mathematics. Volume 97:Issue 9(2020)
• Page Start: 1928
• Page End: 1948
• Publication Date: 2020-09-01
• Subjects: Riesz space fractional derivative -- BDF2 formula -- fourth-order compact operator -- ADI scheme -- stability -- convergence; 26A33 -- 65M06 -- 65M12; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2019.1671587
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : In this paper, a second-order backward difference formula (abbr. BDF2) is used to approximate first-order time partial derivative, the Riesz fractional derivatives are approximated by fourth-order compact operators, a class of new alternating-direction implicit difference scheme (abbr. ADI) is constructed for two-dimensional Riesz space fractional nonlinear reaction–diffusion equation. Stability and convergence of the numerical method are analysed. Numerical experiments demonstrate that the proposed method is effective.