Product integration methods based on discrete spline quasi-interpolants and application to weakly singular integral equations

Chafik Allouch (1) , Paul Sablonnière (2) , Driss Sbibih (1) , M. Tahrichi

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

Quadrature formulae are established for product integration rules based on discrete spline quasi-interpolants on a bounded interval. The integrand considered may have algebraic or logarithmic singularities. These formulae are then applied to the numerical solution of integral equations with weakly singular kernels.

Mots clés: Integral equations; Quadrature formulae; Quasi-interpolation; Singular kernels

Domaines: Analyse numérique [math.NA]

Chafik Allouch, Paul Sablonnière, Driss Sbibih, M. Tahrichi. Product integration methods based on discrete spline quasi-interpolants and application to weakly singular integral equations. Journal of Computational and Applied Mathematics, 2010, 233 (11), pp.2855-2866. ⟨10.1016/j.cam.2009.11.031⟩. ⟨hal-00705489⟩