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A. Gorguis, “A Comparison between Cole-Hopf Transformation and Decomposition Method for Solving Burgers’ Equations,” Applied Mathematics and Computation, Vol. 173, No. 1, 2006, pp. 126-136. doi:10.1016/j.amc.2005.02.045

has been cited by the following article:

• TITLE: A Note on Crank-Nicolson Scheme for Burgers’ Equation

  AUTHORS: Kanti Pandey, Lajja Verma

  KEYWORDS: Hopf-Cole Transformation; Burgers’ Equation; Crank-Nicolson Scheme; Nonlinear Partial Differential Equations

  JOURNAL NAME: Applied Mathematics, Vol.2 No.7, July 15, 2011

  ABSTRACT: In this work we generate the numerical solutions of the Burgers’ equation by applying the Crank-Nicolson method directly to the Burgers’ equation, i.e., we do not use Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. Absolute error of the present method is compared to the absolute error of the two existing methods for two test problems. The method is also analyzed for a third test problem, nu-merical solutions as well as exact solutions for different values of viscosity are calculated and we find that the numerical solutions are very close to exact solution.