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

作者：Mittal R C; Kumar Sumit^*

来源：International Journal of Computer Mathematics, 2010, 87(6): 1326-1337.

DOI：10.1080/00207160802322290

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

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.

• 出版日期2010