Error estimate and extrapolation of a quadrature formula derived from a quartic spline quasi-interpolant
Résumé
In this paper we analyze a quadrature rule based on integrating a C 3 quartic spline quasi-interpolant on a bounded interval which has been introduced in Sablonnière (Rend. Semin. Mat. Univ. Pol. Torino 63(3):107-118, 2005). By studying the sign structure of its associated Peano kernel we derive an explicit formula of the quadrature error with an approximation order O(h 6). A comparison of this rule with the composite Boole's and the three-point Gauss-Legendre rules is given. We also compare the Nyström methods associated with the above quadrature formulae for solving the linear Fredholm integral equation of the second kind. Then, by combining the proposed rule with composite Boole's rule, we construct a new quadrature rule of order O(h 7). All the obtained results are illustrated by several numerical tests.