Fourth-order accurate difference schemes for solving Benjamin–Bona–Mahony–Burgers (BBMB) equation


In this paper, two high-order difference schemes for the Benjamin–Bona–Mahony–Burgers (BBMB) equation are proposed. The first scheme is two level and nonlinear implicit, the second scheme is three level and linear implicit. A priori estimates for the numerical solution are derived. It is proved that the difference schemes are uniquely solvable and unconditionally convergent, in discrete maximum norm, with the convergence order of two in time and four in space. Numerical experiments are given to show the efficiency and accuracy of our methods.

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I 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 Khedidja Bayarassou.

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Bayarassou, K. Fourth-order accurate difference schemes for solving Benjamin–Bona–Mahony–Burgers (BBMB) equation. Engineering with Computers 37, 123–138 (2021).

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  • BBMB equation
  • Nonlinear difference scheme
  • Linearized difference scheme
  • Fourth-order accuracy
  • Unique solvability
  • Convergence