### Keywords : Stability Analysis

##### Stability Analysis in Thin Liquid Film (Immobile Soap Film)

Rotina Jasim Al-Etewi; Zena Talal Al-Nuamy

AL-Rafidain Journal of Computer Sciences and Mathematics, 2011, Volume 8, Issue 2, Pages 13-21
DOI: 10.33899/csmj.2011.163648

This research is dedicated for analyzing the stability of a system of flow equations for soap film that has opposed for disturbance, and this analysis was done by using Galerkin method which enable to find disturbance growth from its nonexistence after making the system linearization. It was shown through the results of analysis that these equations were in stable state when the real part of wave velocity (a)  is a negative quantity, and it is  unstable state when the real part of this velocity is a positive quantity, i.e. a < 0 we get stability and this happens when the distance (do) and the source (uo) in two similar signs and when a > 0 we get unstable state and this happens when do , uo  have two different  signs.

##### Numerical Solution for Sine-Gordon System in One Dimension

Saad A. Manna; Haneen T. Jassim

AL-Rafidain Journal of Computer Sciences and Mathematics, 2010, Volume 7, Issue 2, Pages 47-59
DOI: 10.33899/csmj.2010.163896

This paper has studied the numerical solution for Sine-Gordon system in one dimensions using finite difference methods. We have used Explicit method and Crank-Nicholson method.A comparison between results of the two methods has been done and we obtained that Crank-Nicholson method is more accurate than the Explicit method but the Explicit method is easer .
We also studied the stability analysis for each method by using Fourier(Von-Neumann) method and obtained that Crank-Nicholson method is unconditionally stable while the Explicit  method is stable under the condition    and  .

##### Stability Analysis for Steady State Solutions of Burger Equation

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 Convection & Diffusion equation

AL-Rafidain Journal of Computer Sciences and Mathematics, 2009, Volume 6, Issue 2, Pages 21-31
DOI: 10.33899/csmj.2009.163813

The Stability Analysis of Convection& Diffusion 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 solution is always stable and in the second case the solution is conditionally stable .

##### Numerical Solution and Stability Analysis for Burger's-Huxley Equation

AL-Rafidain Journal of Computer Sciences and Mathematics, 2009, Volume 6, Issue 2, Pages 61-75
DOI: 10.33899/csmj.2009.163797

The Burger’s-Huxley equation has been solved numerically by using two finite difference methods, the explicit scheme and the Crank-Nicholson scheme. A comparison between the two schemes has been made and it has been found that, the first scheme is simpler while the second scheme is more accurate and has faster convergent. Also, the stability analysis of the two methods by using Fourier (Von Neumann) method has been done and the results were that, the explicit scheme is stable under the condition   and the Crank-Nicholson is unconditionally stable.

##### Flow Stability Analysis of the Shallow Water Equations Model

Ashraf S. Aboudi

AL-Rafidain Journal of Computer Sciences and Mathematics, 2009, Volume 6, Issue 2, Pages 101-118
DOI: 10.33899/csmj.2009.163816

This paper is devoted to analyze the stability of shallow water of a system of equations that was exposed to disturbancing. This analysis is done by finding the eigenvalues of the system which enables us to investigate the grow of disturbance after setting shallow water equations in linearization form. It is obtain from the results analysis that the equations are stable when the real part of wave velocity is negative ,and unstable when it is positive.

##### Stability Analysis of Gray-Scott Model in One-dimension

Abbas Y. Al-Bayati; Saad A. Manaa; Abdulghafor M. Al-Rozbayani

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 2, Pages 65-71
DOI: 10.33899/csmj.2008.163972

In this Paper, we studied the stability analysis of steady state solutions of Gray-Scott Model in one-dimension using Fourier mode and we showed that the solutions are conditionally stable.

##### 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.

##### Numerical Solution and Stability Analysis of the Sine-Gordon Equation

Saad Abdullah Manna; Norjan Hasan Juma

AL-Rafidain Journal of Computer Sciences and Mathematics, 2007, Volume 4, Issue 1, Pages 39-56
DOI: 10.33899/csmj.2007.164002

The Sine – Gordon equation has been solved numerically by using two finite differences methods: The first is the explicit scheme and the second is the Crank – Nicholson scheme. A comparison between the two schemes has been made and the results were found to be : the first scheme is simpler and has faster convergence while the second scheme is more accurate . Also , the stability analysis of the two methods by the use of Fourier (Von Neumann) method has been done and the results were found to be : The explicit scheme is conditionally stable if  and the Crank–Nicholson is unconditionally stable .

##### Stability Study of Stationary Solutions of the Viscous Burgers Equation

AL-Rafidain Journal of Computer Sciences and Mathematics, 2007, Volume 4, Issue 1, Pages 19-40
DOI: 10.33899/csmj.2007.163993

Stability study of stationary solutions of the viscous Burgers equation using Fourier mode stability analysis for the stationary solutions , where  is constant and , in two cases is analyzed. Firstly when the wave amplitude  is constant and secondly when the wave amplitude  is variable. In the case of constant amplitude, the results found to be: The solution  is always stable while the solution  is conditionally stable. In the case of variable amplitude, it has been found that the solutions  and  are conditionally stable.

##### 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.

##### Stability of Liquid Film with Negligible Viscosity

Hamsa D. Saleem

AL-Rafidain Journal of Computer Sciences and Mathematics, 2005, Volume 2, Issue 1, Pages 11-19
DOI: 10.33899/csmj.2005.164063

In this paper, we consider the stability analysis for a disturbed unsteady flow, which is two-dimensional incompressible flow in a symmetric film where the effect of viscosity can be neglected in comparison with inertia forces. The partial differential equations governing such flow are obtained from the Navier - Stokes equations and we obtain an analytic solution for those equations. The whole system is disturbed and we found the regions where the flow is stable or unstable.

##### Numerical Solution and Stability Analysis of Huxley Equation

AL-Rafidain Journal of Computer Sciences and Mathematics, 2005, Volume 2, Issue 1, Pages 85-97
DOI: 10.33899/csmj.2005.164070

The numerical solution of Huxley equation by the use of two finite difference methods is done. The first one is the explicit scheme and the second one is the Crank-Nicholson scheme. The comparison between the two methods showed that the explicit scheme is easier and has faster convergence while the Crank-Nicholson scheme is more accurate. In addition, the stability analysis using Fourier (von Neumann) method of two schemes is investigated. The resulting analysis showed that the first scheme is conditionally stable if  and the second scheme is unconditionally stable.

##### Stability Analysis for Steady State Solutions of Huxley Equation

AL-Rafidain Journal of Computer Sciences and Mathematics, 2005, Volume 2, Issue 1, Pages 69-84
DOI: 10.33899/csmj.2005.164069

Stability analysis of steady state solutions of Huxley equation using Fourier mode stability analysis in two cases is investigated. Firstly when the amplitude is constant and secondly when the amplitude is variable and the results were found to be: The solutions and  are  always stable while the solutions  and  are conditionally stable. In the second case, a comparison between the analytical solution and the numerical solution of Galerkin method is done and the results are the same.

##### Stability Analysis for Fluid Flow between Two Infinite Parallel Plates II

Mahdi F. Mosa; Abdo M. Ali

AL-Rafidain Journal of Computer Sciences and Mathematics, 2004, Volume 1, Issue 2, Pages 29-38
DOI: 10.33899/csmj.2004.164109

A model of fluid flow with heat transfer by conduction , convection and radiation has been discussed for stability with respect to restricted parameters (k,a,r,T*) which are proportional to: wave numbers, thermal expansion coefficient, combination of many numbers (Re,Pr,Ec,Bo,W,)and the ratio of walls temperatures, respectively using analytical technique which illustrates that the stability of the system depends on these parameters  and the disturbances with a larger wave number, grows faster than that with smaller wave number .A clear picture of the flow is shown in the velocity field,tables and figures.

##### Stability Analysis for Fluid Flow between Two Infinite Parallel Plates I

Mahdi F. Mosa; Abdo M. Ali

AL-Rafidain Journal of Computer Sciences and Mathematics, 2004, Volume 1, Issue 1, Pages 8-19
DOI: 10.33899/csmj.2004.164093

A model of fluid flow with heat transfer by conduction, convection and radiation has been discussed for stability with respect to restricted parameters (k,a,r,T*) which are proportional to: wave numbers, thermal expansion coefficient, combination of many numbers (Re,Pr,Ec,Bo,W,) and the ratio of walls temperatures, respectively using numerical technique which illustrate that the stability of the system depends on the parameters T* and a. A clear picture of the flow is shown by using an analytical method.