An implicit difference scheme and algorithm implementation for the one-dimensional time-fractional Burgers equations

Wenlin Qiu, Hongbin Chen and Xuan Zheng

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 166, issue C, 298-314

Abstract: An implicit difference scheme with the truncation of order 2−α(0<α<1) for time and order 2 for space is considered for the one-dimensional time-fractional Burgers equations. The L1-discretization formula of the fractional derivative in the Caputo sense is employed. The second-order spatial derivative is approximated by means of the three-point centered formula and the nonlinear convection term is discretized by the Galerkin method based on piecewise linear test functions. The stability and convergence in the L∞ norm are proved by the energy method. Meanwhile, a novel iterative algorithm is proposed and implemented to solve the nonlinear systems. Numerical experiment shows that the results are consistent with our theoretical analysis, and the comparison between the proposed iterative algorithm and the existing methods shows the efficiency of our method.

Keywords: One-dimensional time-fractional Burgers equations; Implicit difference scheme; L1-discretization formula; Stability and convergence; Algorithm implementation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:166:y:2019:i:c:p:298-314

DOI: 10.1016/j.matcom.2019.05.017

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