Numerical solution methods analysis of the Byurgers equation in dissipative environments

Abstract

This research delves into the numerical solution methods employed for analyzing the Burgers equation within dissipative environments. The Burgers equation is a fundamental partial differential equation that finds applications in diverse scientific and engineering disciplines, particularly in modeling nonlinear wave phenomena and fluid dynamics. The presence of dissipative effects, characterized by the kinematic viscosity parameter (v), adds complexity to the equation, necessitating the use of numerical techniques for practical solutions. This study adopts a comprehensive approach to explore various numerical methods, including finite difference, finite element, spectral methods, and others. It seeks to evaluate and compare these methods in terms of their accuracy, stability, and computational efficiency when applied to dissipative environments. The analysis encompasses error assessments, convergence behaviors, and considerations of long-time simulations' stability and efficiency. The ultimate goal of this research is to contribute insights into the selection and application of numerical techniques for solving the Burgers equation in dissipative scenarios. By addressing this critical aspect of mathematical modeling, the study aims to advance our comprehension of complex dissipative systems and foster the development of more precise predictive models across scientific and engineering domains.