Numerical solution of Fredholm Integral and Integro-Differential Equations of the second type

Abstract

In this thesis we consider the numerical approximation of Fredholm integral and integro-differential equations, of the second type. In particular, we use Nystrom's method of collocation in conjunction with classical quadrature schemes, such as the Trapezoidal and Simpson's rules, for approximating the solution of these equations. The novel aspect of the thesis concerns the treatment of singularly perturbed equations, for which a non-uniform Shishkin mesh yields robust, optimal convergence rates, as we demonstrate through numerical experiments.