A New Computational Method Based on the Method of Lines and Adomian Decomposition Method for Burgers' Equation and Coupled System of Burgers' Equations

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DOI: https://doi.org/10.28924/2291-8639-23-2025-44
Published: Feb 14, 2025
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H. O. Bakodah, R. M. Al-Harbi, A. Alshareef, A. A. Alshaery, A New Computational Method Based on the Method of Lines and Adomian Decomposition Method for Burgers' Equation and Coupled System of Burgers' Equations, Int. J. Anal. Appl., 23 (2025), 44.

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H. O. Bakodah, R. M. Al-Harbi, A. Alshareef, A. A. Alshaery

Abstract

This study proposes a new computational scheme for the solution of the class of one-dimensional Burgers’ equations, comprising mainly the classical Burgers’ equation, and the system of coupled Burgers’ equations. This method is based upon coupling the Method of Lines (MOL) and the prominent Adomian Decomposition Method (ADM) for the reliable computational examination of dissimilar initial-boundary value problems of Burgers’ equations. Certainly, MOL helps with the spatial semi-discretization of the governing problem to a system of nonlinear Ordinary Differential Equations (ODEs); while the ADM contributes to the efficient semi-analytical solution of the resulting nonlinear ODEs. Moreover, the computational accuracy of the new approach has been demonstrated on certain test models and further evaluated using L2 and L∞ norms. Indeed, the method produces better results with minimal errors than many existing computational approaches as successfully reported in various supportive figures and tables.

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