Engineering topics
Publications and source records attributed to Guebbai, Hamza.
We study the existence and the uniqueness of the solution of an integro-differential nonlinear Volterra equation with a weakly singular kernel, then using a product integration method with piecewise projection we approximate the solution of this equation.
In this paper, we propose a numerical method to approach the solution of a Fredholm integral equation with a weakly singular kernel by applying the convolution product as a regularization operator and the Fourier series as a projection. Preliminary numerical results show that the order of convergence of the method is better than the one of conventional projection methods.
In this paper, we construct a generalization of the Jacobi iterative method adapted to a system of linear bounded operators. This new method is used with product integration method to solve a linear Fredholm integral equation of the second kind with a weakly singular kernel. The convergence analysis is proved. The numerical tests developed show its effectiveness.