An Efficient Numerical Technique for Solving the Korteweg-de Vries-Burgers Equation

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DOI: https://doi.org/10.28924/2291-8639-23-2025-22
Published: Jan 27, 2025
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Ahmad Alalyani, Dilveen M. Ahmed, Bewar A. Mahmood, An Efficient Numerical Technique for Solving the Korteweg-de Vries-Burgers Equation, Int. J. Anal. Appl., 23 (2025), 22.

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Ahmad Alalyani, Dilveen M. Ahmed, Bewar A. Mahmood

Abstract

Nonlinear partial differential equations, such as the Korteweg-de Vries-Burgers equation (KDVB), receive extensive study in a multitude of fields of engineering and physics. This study presents the Variational Homotopy Perturbation Method (VHPM) as a robust numerical technique for approximating solutions to the KDVB equation. The technique integrates the Variational Iteration Method (VIM) with the Homotopy Perturbation Method (HPM), providing an efficient solution without requiring the discretization or linearization of the equation. The efficacy of the proposed scheme is demonstrated through various problems, with the accuracy of the method being assessed using absolute errors in the  and error norms. The results indicate that the proposed method is straightforward to implement and provides superior outcomes compared to the existing schemes documented in the literature. This study offers a substantial contribution to the advancement of numerical techniques for solving nonlinear partial differential equations, providing beneficial applications across diverse scientific and engineering fields.

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