Keywords : Burger Equation

Stability Analysis for Steady State Solutions of Burger Equation

Saad Abdullah Manna; Badran Jassim Salem

AL-Rafidain Journal of Computer Sciences and Mathematics, 2009, Volume 6, Issue 3, Pages 25-36
DOI: 10.33899/csmj.2009.163836

The Stability Analysis of Steady State Solution of Burger equation by using Fourier mode Stability analysis in two cases has been considered , the first one when the amplitude is constant and the second one when the amplitude is variable .
In the first case the steady state solution is always stable and the second case is conditionally stable . In the second case the comparison between the analytical solution and numerical solution of Galerkin technique are the same.

Numerical Analysis of the Burger Equation using Finite Differences

Saad A. Manna; Badran J. Salem

AL-Rafidain Journal of Computer Sciences and Mathematics, 2007, Volume 4, Issue 1, Pages 119-132
DOI: 10.33899/csmj.2007.164006

The Burger equation had been solved numerically by using two finite differences methods. The first is explicit scheme method and the second is Crank–Nicholson method. A comparison had been made between the two and we find that the Crank–Nicholson method is the best and most accurate than the explicit scheme method, as it is shown in (Table 1). Also the numerical stability for both methods has been made, the explicit scheme method is conditionally stable and the condition is , while Crank–Nicholson method is unconditionally stable.