Keywords : Galerkin Technique


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.
 

Stability Analysis of Steady State Solutions of Sine–Gordon Equation

Saad Abdullah Manna; Norjan Hasan Juma

AL-Rafidain Journal of Computer Sciences and Mathematics, 2007, Volume 4, Issue 2, Pages 11-29
DOI: 10.33899/csmj.2007.164024

The stability analysis of steady state solutions of Sine–Gordon equation using Fourier mode stability analysis in two cases has been considered : Firstly when the amplitude is constant and secondly when the amplitude is variable in the two cases the results were found to be : The steady state solutions  and  are unconditionally stable . In the second case the comparison between the analytical solution and the numerical solution of Galerkin technique has been done . This comparison showed that the analytical solution and the numerical solution of Galerkin technique are the same.
 

Stability Analysis of Fisher Equation Using Numerical Galerkin Techniques

Saad A. Manna; Ahmed F. Qassem

AL-Rafidain Journal of Computer Sciences and Mathematics, 2006, Volume 3, Issue 2, Pages 29-42
DOI: 10.33899/csmj.2006.164057

We studied the stability of the steady state solutions for Fisher Equation in two cases, the First one with constant amplitude and we show that the steady state solution is always stable under any condition, but the other two solutions and  are conditionally stable.
In the Second case, we studied the steady state solutions for various amplitude by using two Methods. The First is analytically by direct Method and the second is numerical method using Galerkin technique which shows the same results, that is the steady state solution  is always stable under any conditions, but the other two solutions and are conditionally stable.