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An Analysis of the Reliability of Error Control B-Spline Gaussian Collocation PDE Software

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Mathematical and Computational Approaches in Advancing Modern Science and Engineering

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Abstract

B-spline Gaussian collocation software for the numerical solution of PDEs has been widely used for several decades. BACOL and BACOLI are recently developed packages of this class that provide control of estimates of the temporal and spatial errors of the numerical solution through the use of adaptive time-stepping/adaptive time integration method order selection and adaptive spatial mesh refinement. Previous studies have investigated the performance of the BACOL and BACOLI packages, primarily with respect to work-accuracy measures. In this paper, we investigate the reliability of the BACOL and BACOLI packages, focusing on the relationship between the requested tolerance and the accuracy achieved. In particular, we consider the effect, on the reliability of the software, of (i) the degree of the piecewise polynomials employed in the representation of the spatial dependence of the approximate solution, (ii) the type of spatial error control employed, and (iii) the type of spatial error estimate computed.

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Authors and Affiliations

  1. Saint Mary’s University, Halifax, NS, B3H 3C3, Canada

    Paul Muir & Jack Pew

Authors
  1. Paul Muir
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  2. Jack Pew
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Correspondence to Paul Muir .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Montreal, Montreal, Québec, Canada

    Jacques Bélair

  2. Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada

    Ian A. Frigaard

  3. Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada

    Herb Kunze

  4. Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Roman Makarov

  5. MS2Discovery Institute, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Roderick Melnik

  6. Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan, Canada

    Raymond J. Spiteri

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Muir, P., Pew, J. (2016). An Analysis of the Reliability of Error Control B-Spline Gaussian Collocation PDE Software. In: Bélair, J., Frigaard, I., Kunze, H., Makarov, R., Melnik, R., Spiteri, R. (eds) Mathematical and Computational Approaches in Advancing Modern Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-30379-6_42

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