A numerical study of stationary solution of viscous Burgers’ equation using wavelet

Abstract

In this paper we have studied the numerical stationary solution of viscous Burgers’ equation with Neumann boundary conditions by applying wavelet Galerkin method. Burns et al. [J. Burns, A. Balogh, D.S. Gilliam, and V. I. Shubov, Numerical stationary solutions for a viscous Burgers’ equation, J. Maths. Sys. Est. Contl. 8 (1998), pp. 1–16] have reported that for moderately small viscosity and for certain initial conditions, numerical solution approaches non-constant shock-type stationary solution though only possible actual stationary solution is a constant. We found that the wavelet Galerkin method precisely captures the correct steady-state solution. The solutions obtained were impressive and verify theoretical results.

Keywords:

• Burgers’ equation
• stationary solution
• compactly supported wavelet
• wavelet Galerkin method
• connection coefficients

Acknowledgements

The second author acknowledges the financial support received from Council of Scientific and Industrial Research, New Delhi (India).