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A new implicit energy conservative difference scheme with fourth-order accuracy for the generalized Rosenau–Kawahara-RLW equation

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Abstract

In the present work, a new implicit fourth-order energy conservative finite difference scheme is proposed for solving the generalized Rosenau–Kawahara-RLW equation. We first design two high-order operators to approximate the third- and fifth-order derivatives in the generalized equation, respectively. Then, the generalized Rosenau–Kawahara-RLW equation is discreted by a three-level implicit finite difference technique in time, and a fourth-order accurate in space. Furthermore, we prove that the new scheme is energy conserved, unconditionally stable, and convergent with \(O(\tau ^{2}+h^{4})\). Finally, two numerical experiments are carried out to show that the present scheme is efficient, reliable, high-order accurate, and can be used to study the solitary wave at long time.

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Authors and Affiliations

  1. School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang, 453003, Henan, People’s Republic of China

    Xiaofeng Wang

  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. Weizhong Dai
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Correspondence to Xiaofeng Wang.

Additional information

Communicated by Armin Iske.

This work was supported in part by the National Natural Science Foundation of China (no. U1304106). The authors thank the reviewers and editor for their many valuable comments and suggestions.

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Wang, X., Dai, W. A new implicit energy conservative difference scheme with fourth-order accuracy for the generalized Rosenau–Kawahara-RLW equation. Comp. Appl. Math. 37, 6560–6581 (2018). https://doi.org/10.1007/s40314-018-0685-4

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  • DOI: https://doi.org/10.1007/s40314-018-0685-4

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