An accurate, robust, and efficient finite difference scheme with graded meshes for the time-fractional Burgers' equation

This work presents the L1 implicit difference scheme based on non-uniform meshes for the time-fractional Burgers equation. We find that the difficulty arising from the singularity of the exact solution at t = 0 can be overcome by non-uniform meshes. We yield the unconditional stability and optimal convergence rate of h(2) + tau(min{r alpha,2-alpha}) by means of the energy method, when selecting r = (2 - alpha)/alpha. Convergence rates are higher than some recently studied schemes. Numerical experiments confirm the predicted theoretical estimate. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper presents an L1 implicit difference scheme based on non-uniform meshes for solving the time-fractional Burgers equation. The difficulty caused by the singularity of the exact solution at t = 0 can be overcome with non-uniform meshes. Through the energy method, the paper derives the unconditional stability and optimal convergence rate, with numerical experiments confirming the theoretical estimate.