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Conservative and fourth-order compact difference schemes for the generalized Rosenau–Kawahara–RLW equation

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Abstract

In this article, we present two conservative and fourth-order compact finite-difference schemes for solving the generalized Rosenau–Kawahara–RLW equation. The proposed schemes are energy-conserved, convergent, and unconditionally stable, and the numerical convergence orders in both \(l_{2}\)-norm and \(l_{\infty }\)-norm are of \(O(\tau ^{2}+h^{4})\). Numerical experiments demonstrate that the present schemes are efficient and reliable.

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Acknowledgements

The first two authors were supported in part by Fujian Province Science Foundation for Middle-aged and Young Teachers (no. JAT190368). The authors would like to thank the anonymous reviewers for their valuable suggestions which improve the quality of the manuscript.

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Authors and Affiliations

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

    Xiaofeng Wang & Hong Cheng

  2. Mathematics and Statistics, College of Engineering and Science, Louisiana Tech University, Ruston, LA, 71272, USA

    Weizhong Dai

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  1. Xiaofeng Wang
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  2. Hong Cheng
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  3. Weizhong Dai
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Correspondence to Xiaofeng Wang.

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Wang, X., Cheng, H. & Dai, W. Conservative and fourth-order compact difference schemes for the generalized Rosenau–Kawahara–RLW equation. Engineering with Computers 38, 1491–1514 (2022). https://doi.org/10.1007/s00366-020-01113-9

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