The Differential Transform Method for Solving the Burgers Equation

Abstract: The Burgers equation is a fundamental partial differential equation (PDE) in applied mathematics, mathematical physics, and engineering, describing a variety of nonlinear wave phenomena such as fluid dynamics, gas dynamics, and traffic flow. Its nonlinear nature makes it a challenging yet fascinating problem to solve analytically or numerically. Among the various methods developed to tackle the Burgers equation, the Differential Transform Method (DTM) has emerged as a powerful semi-analytical technique due to its simplicity, computational efficiency, and ability to handle nonlinear PDEs. This article provides an in-depth exploration of the DTM and its application to solving the Burgers equation, covering its theoretical foundations, implementation, advantages, limitations, and illustrative examples. Keywords: partial differential equation (PDE), Differential Transform Method (DTM), Burgers equation. Title: The Differential Transform 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: 26-30 Research Publish Journals Website: www.researchpublish.com Published Date: 29-April-2025 DOI: https://doi.org/10.5281/zenodo.15304250 Paper Download Link (Source) https://www.researchpublish.com/papers/the-differential-transform-method-for-solving-the-burgers-equation