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Convergence of two conservative high-order accurate difference schemes for the generalized Rosenau–Kawahara-RLW equation

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Abstract

In this paper, we present two high-order accurate difference schemes for the generalized Rosenau–Kawahara-RLW equation. The proposed schemes guarantee the conservation of the discrete energy. The unique solvability of the difference solution is proved. A priori error estimates for the numerical solution is derived. Convergence and stability of the difference schemes are proved. The convergence order is \(O(h^{4} + k^{2} )\) in the uniform norm is discussed without any restrictions on the mesh sizes. Finally, numerical experiments are carried out to support the theoretical claims.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions that helped greatly to improve this article.

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Authors and Affiliations

  1. Mathematics Department, Khurmah University College, Taif University, Taif, Kingdom of Saudi Arabia

    Ahlem Ghiloufi

  2. Institut Supérieur des Sciences Appliquées et de Technologie de Sousse, Université de Sousse, Ibn Khaldoun, 4003, Sousse, Tunisia

    Ahlem Ghiloufi, Mohamed Rahmeni & Khaled Omrani

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  1. Ahlem Ghiloufi
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  2. Mohamed Rahmeni
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  3. Khaled Omrani
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Correspondence to Khaled Omrani.

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Ghiloufi, A., Rahmeni, M. & Omrani, K. Convergence of two conservative high-order accurate difference schemes for the generalized Rosenau–Kawahara-RLW equation. Engineering with Computers 36, 617–632 (2020). https://doi.org/10.1007/s00366-019-00719-y

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