Etude des équations intégrales de Volterra de première espèce en utilisant les techniques des splines

Abstract

as ill-posed problems. Generally a discretization of this equations lead to ill-conditioned linear systems. Moreover a slight perturbation in right hand side lead to enormous change of the solution. In this thesis, we present various regularization methods to obtain a stable solution such as SVD, Tikhonov’s regularization, and Lavrentiev method. Also, we present a new numerical method for solving Volterra linear integral equations of first kind, based on the technical modified Lavrentiev classical method where we find it better than approximation method based on the Taylor expansion, and the spline cubic method. The efficiency of our new numerical method is tested by solving some examples for which the exact solution is known. This allows us to estimate the exactness of our numerical results.