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- H. Saidi, Nacer Khelil, S. Hassouni, A. Zerarka
- Applied Mathematics and Computation
- 2006

- Leila Djerou, Mohamed Batouche, Nacer Khelil, A. Zerarka
- IEEE Congress on Evolutionary Computation
- 2007

- A. Zerarka, H. Saidi, S. Hassouni, N. Bensalah
- Applied Mathematics and Computation
- 2006

This paper deals with an integration method of the Schrödinger equation for the bound states, developed within the context of the recently introduced differential quadratic (DQ) method. It is shown also that this result may be extended to the case of a system of coupled differential equations. An application is also proposed and examined. 2006 Published by… (More)

- A. Zerarka, Nacer Khelil, H. Saidi
- IJSPM
- 2006

In a previous work, we have introduced the generalised integral quadratic method (GIQ) to handle the Volterra’s integral equations in which the interpolating points of Tchebychev have been used. In this paper the particle swarm optimisation (PSO) is considered to improve qualitatively, the solutions. This new approach is investigated and tested with some… (More)

- A. Zerarka, S. Ouamane, A. Attaf
- Applied Mathematics and Computation
- 2010

- A. Zerarka, N. Khelil
- 2009

In the present work, we introduce the particle swarm optimization called (PSO in short) to avoid the Runge’s phenomenon occurring in many numerical problems. This new approach is tested with some numerical examples including the generalized integral quadrature method in order to solve the Volterra’s integral equations. Keywords—Integral equation, particle… (More)

- A. Zerarka, H. Saidi, Nacer Khelil
- ICNC
- 2009

We develop the discrete derivatives representation method (DDR) to find the physical structures of the Schrödinger equation in which the interpolation polynomial of Bernstein has been used. In this paper the particle swarm optimization (PSO for short) has been suggested as a means to improve qualitatively the solutions. This approach is carefully handled… (More)

- B. Nine, O. Haif-Khaif, A. Zerarka
- Applied Mathematics and Computation
- 2006

In a previous work, we have introduced the generalized differential quadratic method (called GDQ) to handle the Schrödinger equation. This paper deals with a particular situation in which an application to the non polynomial potential is considered. The results are compared with some numerical examples for the same potential of interest.

- A. Zerarka
- 2009

Exact solutions to a class of nonlinear wave equations are established using the functional variable method. This method is a powerful tool to the search of exact traveling solutions in closed form.We show that, the method is straightforward and concise for several kind of nonlinear problems. Some specific examples arising in a number of physical problems… (More)