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Nonlinear improvements of quasi-interpolanting splines to approximate piecewise smooth functions

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  • Aràndiga, Francesc
  • Donat, Rosa
  • López-Ureña, Sergio

Abstract

Quasi-interpolation based on B-spline approximation methods are used in numerous applications. However, we observe that the Gibbs phenomenon appears when approximating near discontinuities. We present nonlinear modifications, based on weighted essentially non-oscillatory (WENO) techniques, of well-known quasi-interpolation methods to avoid this phenomena near discontinuities and, at the same time, maintain the high-order accuracy in smooth regions.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:448:y:2023:i:c:s0096300323001157
    DOI: 10.1016/j.amc.2023.127946
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Aràndiga, F. & Barrera, D. & Eddargani, S. & Ibáñez, M.J. & Roldán, J.B., 2024. "Non-uniform WENO-based quasi-interpolating splines from the Bernstein–Bézier representation and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 158-170.

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