Pointwise error estimate and stability analysis of fourth-order compact difference scheme for time-fractional Burgers’ equation

Qifeng Zhang, Cuicui Sun, Zhi-Wei Fang and Hai-Wei Sun

Applied Mathematics and Computation, 2022, vol. 418, issue C

Abstract: A novel implicit high-order compact difference scheme is established for the time-fractional Burgers’ equation based on a newly developed nonlinear compact operator and the reduction order technique under the uniform mesh and graded mesh. Uniqueness, boundedness, convergence in the pointwise sense and stability in L2-norm of the discrete solutions are proved by the Browder fixed point theorem and energy argument. Numerical examples with the smooth solution and nonsmooth solution are provided to confirm numerical theoretical results and demonstrate the efficiency of the high-order compact difference scheme.

Keywords: Fractional Burgers’ equation; Compact difference scheme; Reduction order method; Pointwise error estimate (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321009073

DOI: 10.1016/j.amc.2021.126824

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