Quadratic spline quasi-interpolants and collocation methods

Françoise Foucher (1) , Paul Sablonnière (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 IRMAR - Institut de Recherche Mathématique de Rennes

Univariate and multivariate quadratic spline quasi-interpolants provide interesting approximation formulas for derivatives of approximated functions that can be very accurate at some points thanks to the superconvergence properties of these operators. Moreover, they also give rise to good global approximations of derivatives on the whole domain of definition. From these results, some collocation methods are deduced for the solution of ordinary or partial differential equations with boundary conditions. Their convergence properties are illustrated on some numerical examples of elliptic boundary value problems.

Mots clés: Spline approximants; Numerical differentiation; Spline collocation methods.; Spline collocation methods

Domaines: Analyse numérique [math.NA]

Françoise Foucher, Paul Sablonnière. Quadratic spline quasi-interpolants and collocation methods. Mathematics and Computers in Simulation, 2009, 79 (12), pp.3455-3465. ⟨10.1016/j.matcom.2009.04.004⟩. ⟨hal-00468155⟩