Numerical Methods for the Time Fractional Convection-Diffusion-Reaction Equation. (27th July 2021)

• Record Type: Journal Article
• Authors: Li, Changpin; Wang, Zhen
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 10(2021)
• Page Start: 1115
• Page End: 1153
• Publication Date: 2021-07-27
• Subjects: Caputo derivative -- convergence -- local discontinuous Galerkin method -- non-uniform time mesh -- stability; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1936019
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, efficient methods are derived for seeking numerical solution to the time fractional convection-diffusion-reaction equation whose solution very likely exhibits a weak regularity at the starting time. Here, the time fractional derivative in the Caputo sense with order in (0, 1) is discretized by the finite difference methods with uniform and non-uniform meshes and the spatial derivative by the local discontinuous Galerkin finite element method. The derived numerical schemes are stable and convergent. Finally, some numerical experiments are presented to verify the theoretical analysis.