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Quadratic spline quasi-interpolants and collocation methods

Author

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  • Foucher, Françoise
  • Sablonnière, Paul

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.

Suggested Citation

  • Foucher, Françoise & Sablonnière, Paul, 2009. "Quadratic spline quasi-interpolants and collocation methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3455-3465.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:12:p:3455-3465
    DOI: 10.1016/j.matcom.2009.04.004
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    Citations

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    Cited by:

    1. Bouhiri, S. & Lamnii, A. & Lamnii, M., 2019. "Cubic quasi-interpolation spline collocation method for solving convection–diffusion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 33-45.
    2. Boujraf, A. & Tahrichi, M. & Tijini, A., 2015. "C1 Superconvergent quasi-interpolation based on polar forms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 102-115.
    3. Sbibih, D. & Serghini, A. & Tijini, A., 2015. "Superconvergent local quasi-interpolants based on special multivariate quadratic spline space over a refined quadrangulation," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 145-156.
    4. Allouch, C. & Boujraf, A. & Tahrichi, M., 2017. "Superconvergent spline quasi-interpolants and an application to numerical integration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 137(C), pages 90-108.
    5. Aràndiga, Francesc & Donat, Rosa & López-Ureña, Sergio, 2023. "Nonlinear improvements of quasi-interpolanting splines to approximate piecewise smooth functions," Applied Mathematics and Computation, Elsevier, vol. 448(C).

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