Keywords : Fourier (Von Neumann) method


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.
 

The Finite Difference Methods for φ4 Klein-Gordon Equation

Saad A. Manaa; Laya Y. Hawell

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 2, Pages 47-63
DOI: 10.33899/csmj.2008.163970

We solved φ4 Klein-Gordon equation numerically by using two finite difference methods: The first is the explicit method and the second is the implicit (Crank-Nicholson) method. Also, we studied the numerical stability of the two methods using Fourier (Von Neumann) method and it has been found that the first method is simpler and has faster convergence while the second method is more accurate, and the explicit method is conditionally stable while the implicit method 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 .