A collocation method for the numerical solution of a two dimensional integral equation using a quadratic spline quasi-interpolant

Authors:
Chafik Allouch;Paul Sablonnière;Driss Sbibih
Affiliations:
ESTO, Laboratoire MATSI, Equipe ANTI-URAC05, Université Mohammed I, Oujda, Morocco;INSA de Rennes, Centre de Mathématiques, Rennes, France;ESTO, Laboratoire MATSI, Equipe ANTI-URAC05, Université Mohammed I, Oujda, Morocco
Venue:
Numerical Algorithms
Year:
2013

Citing 2
Cited 0

A fast numerical solution method for two dimensional Fredholm integral equations of the second kind

Applied Numerical Mathematics
Quadratic spline quasi-interpolants and collocation methods

Mathematics and Computers in Simulation

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Abstract

In this paper, we propose an interesting method for approximating the solution of a two dimensional second kind equation with a smooth kernel using a bivariate quadratic spline quasi-interpolant (abbr. QI) defined on a uniform criss-cross triangulation of a bounded rectangle. We study the approximation errors of this method together with its Sloan's iterated version and we illustrate the theoretical results by some numerical examples.