IJPAM: Volume 69, No. 1 (2011)

A GALERKIN'S PERTURBATION TYPE METHOD TO
APPROXIMATE A FIXED POINT OF
A COMPACT OPERATOR

L. Grammont
Laboratoire de Mathématiques
l'Université de St-Étienne
EA3989, Membre d'Université de Lyon
23, Rue Dr. Paul Michelon, St-Étienne, 42023, FRANCE
e-mail: [email protected]


Abstract. We propose a fixed point approximation of a compact operator. It is adapted from the method proposed by R.P. Kulkarni for linear operator equations. It is proved to be superconvergent, while the iterated Galerkin method, proposed by K.E. Atkinson and F.A. Potra, needs an additional assumption in order to be superconvergent.

Received: March 2, 2010

AMS Subject Classification: 41A35, 47H10, 47J25

Key Words and Phrases: fixed point equation, superconvergence, Galerkin approximation, iterated Galerkin approximation

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 1