Quadratic spline quasi-interpolants and collocation methods

Françoise Foucher and Paul Sablonnière

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 79, issue 12, 3455-3465

Abstract: 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 and compared with finite difference methods on some numerical examples of elliptic boundary value problems.

Keywords: Spline approximants; Numerical differentiation; Spline collocation methods (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2009:i:12:p:3455-3465

DOI: 10.1016/j.matcom.2009.04.004

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