A posteriori error estimation and adaptive strategy for a nonlinear fractional differential equation. Issue 2 (1st February 2022)

• Record Type: Journal Article
• Authors: Liu, Li-Bin; Chen, Yanping
• Is Part Of: International journal of computer mathematics. Volume 99:Issue 2(2022)
• Page Start: 240
• Page End: 246
• Publication Date: 2022-02-01
• Subjects: Caputo fractional derivative -- finite difference -- adaptive grid -- a posteriori error estimation -- monitor function; 65L05 -- 65L12 -- 65L20; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2021.1906420
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : A nonlinear fractional differential equation with Caputo fractional derivative is considered. The problem is discretized by an upwind finite difference scheme for which a posteriori error analysis in the maximum norm is derived. A partly heuristic argument based on this a posteriori error estimation leads to several suitable monitor functions, and a new monitor function is constructed to design an adaptive grid algorithm. Numerical results are presented to illustrate the performance of the presented adaptive method. Compared with the other monitor functions, the presented adaptive grid method based on the new monitor function is more suitable to solve this type of nonlinearfractional differential equation.