A systematic literature review of Burgers’ equation with recent advances

Pramana: Journal of physics

MAYUR P BONKILE^1¹  ASHISH AWASTHI^2² 

[1] Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India^1;Department of Mathematics, National Institute of Technology Calicut, Kozhikode 673 601, India^2

关键词: Burgers’ equation;    non-linear convection–diffusion equation;    Hopf–Cole transformation;    numerical solutions;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Even if numerical simulation of the Burgers’ equation is well documented in the literature, a detailed literature survey indicates that gaps still exist for comparative discussion regarding the physical and mathematical significance of the Burgers’ equation. Recently, an increasing interest has been developed within the scientific community, for studying non-linear convective–diffusive partial differential equations partly due to the tremendous improvement in computational capacity. Burgers’ equation whose exact solution is well known, is one of the famous non-linear partial differential equations which is suitable for the analysis of various important areas. A brief historical review of not only the mathematical, but also the physical significance of the solution of Burgers’ equation is presented, emphasising current research strategies, and the challenges that remain regarding the accuracy, stability and convergence of various schemes are discussed. One of the objectives of this paper is to discuss the recent developments in mathematical modelling of Burgers’ equation and thus open doors for improvement. No claim is made that the content of the paper is new. However, it is a sincere effort to outline the physical and mathematical importance of Burgers’ equation in the most simplified ways. We throw some light on the plethora of challenges which need to be overcome in the research areas and give motivation for the next breakthrough to take place in a numerical simulation of ordinary/partial differential equations.

【 授权许可】

CC BY