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.