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The Extrapolated Crank–Nicolson Orthogonal Spline Collocation Method for a Quasilinear Parabolic Problem with Nonlocal Boundary Conditions

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Abstract

For a quasilinear parabolic problem in one space variable with nonlocal boundary conditions, we formulate and analyze the extrapolated Crank–Nicolson orthogonal spline collocation method with \(C^1\) splines of degree \(\ge \)3. We establish an optimal order error bound in the discrete maximum norm in time and the continuous maximum norm in space. We present numerical results which confirm the theoretical analysis and exhibit superconvergence.

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO , 80401-1887, USA

    B. Bialecki

  2. Mathematical Reviews, American Mathematical Society, 416 Fourth Street, Ann Arbor, MI , 48103, USA

    G. Fairweather

  3. Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Valladolid, Valladolid, Spain

    J. C. López-Marcos

Authors
  1. B. Bialecki
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  2. G. Fairweather
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  3. J. C. López-Marcos
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Correspondence to G. Fairweather.

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Bialecki, B., Fairweather, G. & López-Marcos, J.C. The Extrapolated Crank–Nicolson Orthogonal Spline Collocation Method for a Quasilinear Parabolic Problem with Nonlocal Boundary Conditions. J Sci Comput 62, 265–283 (2015). https://doi.org/10.1007/s10915-014-9853-x

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  • DOI: https://doi.org/10.1007/s10915-014-9853-x

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