On the numerical solution of two-dimensional Rosenau–Burgers (RB) equation

Abstract

Our purpose is to solve numerically the nonlinear evolutionary problem called Rosenau–Burgers (RB) equation. First, we have derived error estimates of semidiscrete finite element method for the approximation of the Rosenau–Burgers problem. For a second-order accuracy in time, we propose the Galerkin–Crank–Nicolson fully discrete method. Second, a linearized difference scheme for the Rosenau–Burgers equation is considered. It is proved that the proposed difference scheme is uniquely solvable, and the method is shown to be second-order convergent both in time and space in maximum norm. Finally, some numerical experiments are given to demonstrate the validity and accuracy of our linearized difference scheme.

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Acknowledgements

We would like to thank the reviewers that their comments and suggestions have really improved the quality of the paper.

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Correspondence to Khaled Omrani.

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Omrani, K., Debebria, H. & Bayarassou, K. On the numerical solution of two-dimensional Rosenau–Burgers (RB) equation. Engineering with Computers (2020). https://doi.org/10.1007/s00366-020-01055-2

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Keywords

  • Rosenau–Burgers equation
  • Finite element method
  • Semidiscrete scheme
  • Fully discrete method
  • Linearized difference scheme
  • Error estimates

Mathematics Subject Classification

  • 65M06
  • 65M12
  • 65M15