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A new linearized fourth-order conservative compact difference scheme for the SRLW equations

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Abstract

In this paper, a novel three-point fourth-order compact operator is considered to construct new linearized conservative compact finite difference scheme for the symmetric regularized long wave (SRLW) equations based on the reduction order method with three-level linearized technique. The discrete conservative laws, boundedness and unique solvability are studied. The convergence order \(\mathcal {O}(\tau ^{2}+h^{4})\) in the \(L^{\infty }\)-norm and stability of the present compact scheme are proved by the discrete energy method. Numerical examples are given to support the theoretical analysis.

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Acknowledgements

The authors would like to thank Prof. Weizhong Dai (Louisiana Tech University), Prof. Hongtao Chen (Xiamen University) and the referees for their valuable discussions and suggestions which improve the quality of the manuscript.

Funding

This work is supported by the Natural Science Foundation of Fujian Province, China (No. 2020J01796). The first author was supported by the Institute of Meteorological Big Data-Digital Fujian and Fujian Key Laboratory of Data Science and Statistics.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian, 363000, People’s Republic of China

    Yuyu He, Xiaofeng Wang & Ruihua Zhong

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  1. Yuyu He
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  2. Xiaofeng Wang
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  3. Ruihua Zhong
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Correspondence to Xiaofeng Wang.

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Communicated by: Enrique Zuazua

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He, Y., Wang, X. & Zhong, R. A new linearized fourth-order conservative compact difference scheme for the SRLW equations. Adv Comput Math 48, 27 (2022). https://doi.org/10.1007/s10444-022-09951-5

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