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September 5, 2026International Journal of Modelling and Simulation

A meshless method for the nonlinear Benjamin–Bona–Mahony–Burgers equation: a basic model for long waves in a nonlinear dispersive medium

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Authors

FSFarzaneh SafariMFMojtaba FardiMHMousa J. Huntul

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Overview

Computational modeling demonstrates accurate solitary wave solutions for the nonlinear Benjamin–Bona–Mahony–Burgers equation, highlighting the stability of trigonometric basis functions.

Key Points

  • Develop a stable and accurate meshless numerical technique to solve the nonlinear Benjamin–Bona–Mahony–Burgers equation describing long-wave propagation in dispersive media.
  • Transformed the nonlinear governing equation into a linear system solved via an adapted backward substitution method (BSM).
  • Approximated time derivatives using a finite difference scheme and formulated spatial wave solutions using trigonometric basis functions (TBFs).
  • Evaluated numerical convergence and stability across varying scaling parameters of the basis functions.
  • Successfully derived solitary wave solutions without relying on standard computational mesh grids.
  • Demonstrated robust numerical stability and high solution accuracy under testing with the BBM-Burgers equation.

Cite This Study

Safari et al. (2026) studied this question.

synapsesocial.com/papers/6a9bd4606b95aff0620ebfd8https://doi.org/10.1080/02286203.2026.2726374
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