Séminaire Stéphanois de Mathématiques Accessibles

Solution of Integral Equations using Projection Methods

by Rekha Kulkarni (IIT Bombay)

C112 (Faculté des sciences de Saint-Etienne)


Faculté des sciences de Saint-Etienne

23 rue du docteur Paul Michelon, Saint-Etienne
We are interested in approximate solutions of the Fredholm integral equations of the second kind using projection methods. Classical methods such as the Galerkin method associated with an orthogonal projection and the collocation method associated with an interpolatory projection are discussed. We also consider the iterated Galerkin and the iterated collocation methods which have higher orders of convergence. A method proposed by author which improves upon the iterated Galerkin/iterated collocation is next described. The proofs for orders of convergence for various methods in the case of a smooth kernel are discussed briefly. We obtain orders of convergence in the case of a kernel of the type of a Green's function and validate these results by a numerical example. Prerequisite: Niveau d'Analyse L3