A modified Kulkarni's method based on a discrete spline quasi-interpolant

Chafik Allouch (1) , Paul Sablonnière (2) , Driss Sbibih (1)

1 Université Mohammed Premier [Oujda]
2 IRMAR - Institut de Recherche Mathématique de Rennes

We use a discrete spline quasi-interpolant (abbr. dQI) defined on a bounded interval for the numerical solution of linear Fredholm integral equations of the second kind with a smooth kernel by collocation and a modified Kulkarni's method together with its Sloan's iterated version. We study the approximation errors of these methods and we illustrate the theoretical results by a numerical example.

Mots clés: Integral equation; Quasi-interpolation; Collocation

Domaines: Analyse numérique [math.NA]

Chafik Allouch, Paul Sablonnière, Driss Sbibih. A modified Kulkarni's method based on a discrete spline quasi-interpolant. Mathematics and Computers in Simulation, 2011, 81 (10), pp.1991-2000. ⟨10.1016/j.matcom.2010.12.17⟩. ⟨hal-00705480⟩