Work

A Compact Finite Difference Scheme with Second-Order Temporal and Sixth-Order Spatial Accuracy for Variable-Order Time-Fractional Sub-Diffusion Equations

Year: 2026

Type: article

Abstract: In this paper, a finite difference scheme is proposed for the variable-order time-fractional sub-diffusion equation, achieving second-order accuracy in time and sixth-order accuracy in space. For spatial discretization, a newly constructed operator A is employed to obtain a sixth-order compact approximation of the second derivative. Using an energy analysis method, a priori estimates of the scheme are derived, and the unconditional stability and convergence are rigorously proved. Numerical examples are provided to verify the theoretical accuracy of the scheme.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract10050347

Authors: Yu Bo, Xin Zhang, Yu Wang, Yuanfeng Jin

Institution: Yanbian University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funder: Natural Science Foundation of Jilin Province