—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.
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)
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)
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)