A high-order L2 type difference scheme for the time-fractional diffusion equation

2021/02/17 by Anatoly A. Alikhanov, Chengming Huang, Alikhanov, Anatoly A. +1 · 1 citation
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2102.08813

openalex publication_date 2021/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The present paper is devoted to constructing L2 type difference analog of the Caputo fractional derivative. The fundamental features of this difference operator are studied and it is used to construct difference schemes generating approximations of the second and fourth order in space and the (3-α) th-order in time for the time fractional diffusion equation with variable coefficients. Stability of the schemes under consideration as well as their convergence with the rate equal to the order of the approximation error are proven. The received results are supported by the numerical computations performed for some test problems.

Citations

• Fractional Differential Equations

Cited by

• Numerical Identification of a Time-Dependent Coefficient in a Time-Fractional Diffusion Equation with Integral Constraints

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