A Note on Crank-Nicolson Scheme for Burgers’ Equation

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.

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.

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.

nullK. Pandey and L. Verma, "A Note on Crank-Nicolson Scheme for Burgers’ Equation,"

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