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A semi-implicit finite difference scheme for the multi-term time-fractional Burgers-type equations

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Abstract

The main purpose of this paper is to construct a semi-implicit difference scheme for the multi-term time-fractional Burgers-type equations. Firstly, the L2-discretization formula is applied to the discretization of the multi-term Caputo fractional derivatives. Secondly, the second-order spatial derivative is approximated by using the second-order central difference quotient approximation and the nonlinear convection term \(uu_x\) is discretized via the semi-implicit method. Then, a fully discrete finite difference scheme is established. The unconditional stability and convergence in maximum-norm are derived by the discrete energy method and the mathematical induction. Numerical experiments are performed to validate the theoretical analysis.

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Acknowledgements

The author is very grateful for the reviewers’ valuable comments and suggestions. This article is supported by the Construct Program of the Key Discipline in Hunan Province, Performance Computing and Stochastic Information Processing (Ministry of Education of China).

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  1. Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, China

    Wen Zhang

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Zhang, W. A semi-implicit finite difference scheme for the multi-term time-fractional Burgers-type equations. J. Appl. Math. Comput. 65, 813–830 (2021). https://doi.org/10.1007/s12190-020-01416-6

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  • DOI: https://doi.org/10.1007/s12190-020-01416-6

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