A Note on Crank-Nicolson Scheme for Burgers’ Equation

Kanti  Pandey; Lajja  Verma

doi:10.4236/am.2011.27118

Kanti Pandey, Lajja Verma

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.

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

Cite this paper: nullK. Pandey and L. Verma, "A Note on Crank-Nicolson Scheme for Burgers’ Equation," Applied Mathematics, Vol. 2 No. 7, 2011, pp. 883-889. doi: 10.4236/am.2011.27118.

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