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A numerical solution for a class of time fractional diffusion equations with delay

V. Pimenov,A. Hendy

2017 · DOI: 10.1515/amcs-2017-0033
International Journal of Applied Mathematics and Computer Sciences · 24 Citations

TLDR

The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4) in L∞-norm is the main purpose of this study, which focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method.

Abstract

Abstract This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4) in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.