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Unconditional Convergence in Maximum-Norm of a Second-Order Linearized Scheme for a Time-Fractional Burgers-Type Equation

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Abstract

We study linearized finite difference scheme for a time-fractional Burgers-type equation in this paper. A linearized scheme with second-order accuracy in time and space is proposed. The advantage of the scheme is that iterative method is not required for finding the approximated solutions. Nonlinearity involving derivatives causes difficulties in analysis. By refined estimates of our previous study, we show that the scheme unconditionally converges with second-order in maximum-norm. The theoretical results are justified by numerical tests.

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Acknowledgements

The authors would like to thank the two anonymous reviewers for careful reading on our manuscript. Their valuable comments, particularly the suggestions on the comparison of the proposed scheme with its two level variant (on the diffusion term), have inspired us to improve significantly the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Macau, Avenida da Universidade, Macau, China

    Seakweng Vong & Pin Lyu

Authors
  1. Seakweng Vong
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  2. Pin Lyu
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Correspondence to Pin Lyu.

Additional information

S. Vong: This research is supported by the Macao Science and Technology Development Fund 010/2015/A and 050/2017/A and the Grant MYRG2017-00098-FST from University of Macau.

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Vong, S., Lyu, P. Unconditional Convergence in Maximum-Norm of a Second-Order Linearized Scheme for a Time-Fractional Burgers-Type Equation. J Sci Comput 76, 1252–1273 (2018). https://doi.org/10.1007/s10915-018-0659-0

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  • DOI: https://doi.org/10.1007/s10915-018-0659-0

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