On the numerical solution of the Burgers's equation

Abstract

In this paper, we consider the linear heat equation arisen from the Burgers's equation using the Hopf–Cole transformation. Discretization of this equation with respect to the space variable results in a linear system of ordinary differential equations. The solution of this system involves in computing exp(α A)y for some vector y, where A is a large special tridiagonal matrix and α is a positive real number. We give an explicit expression for computing exp(α A)y. Finally, some numerical experiments are given to show the efficiency of the method.

Keywords:

• Burgers’ equation
• Hopf–Cole transformation
• semi-discretization
• system of ODEs
• matrix exponential

2000 AMS Subject Classification :

• 35K55
• 15A15

Acknowledgements

The author would like to thank one of the referees for his (or her) helpful comments.