Solution of Integral Equations using Projection Methods
par
Rekha Kulkarni(IIT Bombay)
→
Europe/Paris
C112 (Faculté des sciences de Saint-Etienne)
C112
Faculté des sciences de Saint-Etienne
23 rue du docteur Paul Michelon, Saint-Etienne
Description
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