Exploring Mathematical Modeling of Non-linear Inviscid and Viscid Burgers’ Equations: A Comprehensive Study

Articles in Press

Document Type : Research Paper

Author

Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Charotar University of Science and Technology, Changa-388421, Gujarat, India.

Abstract

Present study investigates the application of the power series method to solve non-linear inviscid
and viscid Burgers’ equations, a fundamental equation for modeling various physical phenomena that include fluid dynamics and traffic flow. We derive approximate solutions under specific initial conditions, demonstrating the effectiveness of the power series approach for obtaining accurate results. The solutions obtained are expressed in series form, which can be further simplified into closed analytic forms. Our findings indicates that the accuracy of the derived solutions improves with the inclusion of additional terms in the series expansion. This research highlights the advantages of the power series method in solving a robust mathematical tool for addressing dynamical systems with non-linearity. It provides solution with accuracy, efficiency, and minimal computations.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 29 May 2026

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History

  • Receive Date: 29 May 2025
  • Revise Date: 16 April 2026
  • Accept Date: 25 May 2026

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