Modified Burgers' Equation: Numerical Simulations Using Finite Difference Techniques

Author(s)	Dr. Anil Kumar, Mr. Satrughan Kumar
Country	India
Abstract	This paper discusses the formulation of the Modified Burgers' equation, the mathematical methods for solving it, and presents finite difference techniques for its numerical simulation. Furthermore, the paper examines the challenges and advantages of these numerical methods, particularly in terms of accuracy and efficiency. The Burgers' equation is a fundamental partial differential equation (PDE) that appears in various fields of Mathematics, physics and engineering, such as fluid dynamics, nonlinear acoustics, and traffic flow. The modified Burgers' equation introduces additional terms to the classical Burgers' equation, making it more suitable for modelling complex phenomena. Numerical simulations using finite difference techniques are crucial in solving the Modified Burgers' equation due to its nonlinear nature. This paper explores the numerical simulation of the modified Burgers' equation using finite difference techniques. The mathematical formulation of the modified Burgers' equation, the discretization process using finite difference methods, and the implementation of numerical schemes are discussed. The results of numerical simulations are presented, and the accuracy and stability of the methods are analysed.
Keywords	Burgers' Equation, Finite Difference Techniques, Stability, Numerical
Field	Mathematics
Published In	Volume 17, Issue 1, January-March 2026
Published On	2026-01-16

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