Pointwise error estimates of compact difference scheme for mixed-type time-fractional Burgers’ equation

Xiangyi Peng, Da Xu and Wenlin Qiu

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 208, issue C, 702-726

Abstract: In this paper, based on the developed nonlinear fourth-order operator and method of order reduction, a novel fourth-order compact difference scheme is constructed for the mixed-type time-fractional Burgers’ equation, from which L1-discretization formula is applied to deal with the terms of fractional derivative, and the nonlinear convection term is discretized by nonlinear compact difference operator. Then a fully discrete L1 compact difference scheme on uniform meshes can be established by approximating spatial second-order derivative with classic compact difference formula. The convergence and stability of the proposed scheme are rigorously proved in the L∞-norm by the energy argument and mathematical induction. We also establish a temporal second-order compact difference scheme on graded time meshes for solving the problem with weak initial singularity. Finally, several numerical experiments are provided to test the accuracy of two numerical schemes and verify the theoretical analysis.

Keywords: Mixed-type time-fractional Burgers’ equation; Compact difference schemes; Pointwise error estimate; Stability; Numerical experiments (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:208:y:2023:i:c:p:702-726

DOI: 10.1016/j.matcom.2023.02.004

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