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- 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.

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

- 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

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

- K. Mahboub, A. Zerarka, V. G. Foester
- 2003

In our model we have used the Langevin equation in order to study the interaction of a charged particle () with a gas of electrons. We have deduced an analytic expression for the electronic stopping power and the corresponding range. We have introduced a new concept that of the electronic friction and the deduction of its analytic expression. Our model… (More)

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. RESUME Dans un… (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)

- Y. Boumedjane, H. Saidi, S. Hassouni, A. Zerarka
- Applied Mathematics and Computation
- 2007

- 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)