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Optimal superconvergent one step quadratic spline collocation methods

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Abstract

We formulate new optimal quadratic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the collocation equations can be solved using a matrix decomposition algorithm. The results of numerical experiments exhibit the expected optimal global accuracy as well as superconvergence phenomena.

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Authors and Affiliations

  1. Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO, 80401-1887, USA

    B. Bialecki & G. Fairweather

  2. Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678, Nicosia, Cyprus

    A. Karageorghis

  3. Avanade Inc., 2211 Elliott Avenue, Seattle, WA, 98121, USA

    Q.N. Nguyen

Authors
  1. B. Bialecki
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  2. G. Fairweather
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  3. A. Karageorghis
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  4. Q.N. Nguyen
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Corresponding author

Correspondence to G. Fairweather.

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AMS subject classification (2000)

65N35, 65N22

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Bialecki, B., Fairweather, G., Karageorghis, A. et al. Optimal superconvergent one step quadratic spline collocation methods . Bit Numer Math 48, 449–472 (2008). https://doi.org/10.1007/s10543-008-0188-6

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  • DOI: https://doi.org/10.1007/s10543-008-0188-6

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