Keywords : Explicit Scheme


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

Saad A. Manaa; Farhad M. Saleem

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.
 

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 .
 

Numerical Solution and Stability Analysis of Huxley Equation

Saad A. Manaa; Mohammad Sabawi

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.