A Comparative Analysis of the Differential Transform Method and the Adomian Decomposition Method for Solving the Burgers Equation

Abstract: The Burgers equation, a fundamental partial differential equation (PDE) in applied mathematics and physics, is widely studied due to its applications in fluid dynamics, gas dynamics, traffic flow, and nonlinear wave propagation. Named after Johannes Martinus Burgers, this equation combines nonlinear convection and diffusion, making it a simplified model for complex phenomena like turbulence and shock waves. The one-dimensional Burgers equation is typically expressed as: where represents the velocity field, is the kinematic viscosity, is time, and is the spatial coordinate. The nonlinear term introduces complexity, making analytical solutions challenging except in specific cases. As a result, semi-analytical and numerical methods have been developed to approximate solutions to the Burgers equation. Among these methods, the Differential Transform Method (DTM) and the Adomian Decomposition Method (ADM) are two powerful semi-analytical techniques that have gained attention for their ability to handle nonlinear PDEs efficiently. This article provides a detailed comparison of DTM and ADM when applied to the Burgers equation, examining their theoretical foundations, implementation procedures, advantages, limitations, and performance in terms of accuracy, computational efficiency, and applicability. Keywords: Differential Transform Method (DTM), Adomian Decomposition Method (ADM), Burgers equation. Title: A Comparative Analysis of the Differential Transform Method and the Adomian Decomposition Method for Solving the Burgers Equation Author: Ahmad M. D. Al-Eybani International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Vol. 13, Issue 1, April 2025 - September 2025 Page No: 20-25 Research Publish Journals Website: www.researchpublish.com Published Date: 29-April-2025 DOI: https://doi.org/10.5281/zenodo.15303937 Paper Download Link (Source) https://www.researchpublish.com/papers/a-comparative-analysis-of-the-differential-transform-method-and-the-adomian-decomposition-method-for-solving-the-burgers-equation