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https://doi.org/10.1007/s12043-018-1559-4

has been cited by the following article:

• TITLE: Numerical Method for Non-Linear Conservation Laws: Inviscid Burgers Equation

  AUTHORS: R. Hemel, M. T. Azam, M. S. Alam

  KEYWORDS: Conservation Law, Inviscid Burgers Equation, Shock Wave, Rarefaction Wave, Finite Volume Method

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.9 No.6, June 29, 2021

  ABSTRACT: This paper deals with the Burgers equation which is the most common model used in the nonlinear conservation laws. Here the theoretical aspect of conservation law is discussed by using inviscid Burgers equation. At first, we introduce the general non-linear conservation law as a partial differential equation and its solution procedure by the method of characteristic. Next, we present the weak solution of the problem with entropy condition. Taking into account shock wave and rarefaction wave, the Riemann problem has also been discussed. Finally, the finite volume method is considered to approximate the numerical solution of the inviscid Burgers equation with continuous and discontinuous initial data. An illustration of the problem is provided by some examples. Moreover, the Godunov method provides a good approximation for the problem.