research-article

Optimal Superconvergent One Step Nodal Cubic Spline Collocation Methods

Authors:

Bernard Bialecki,

Graeme Fairweather,

Andreas KarageorghisAuthors Info & Claims

SIAM Journal on Scientific Computing, Volume 27, Issue 2

Pages 575 - 598

https://doi.org/10.1137/040609793

Published: 01 January 2005 Publication History

Abstract

We formulate new optimal (fourth) order one step nodal cubic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the respective collocation equations can be solved using matrix decomposition algorithms (MDAs). MDAs are fast, direct methods which employ fast Fourier transforms and require O(N² log N) operations on an $N \times N$ uniform partition of the unit square. The results of numerical experiments exhibit expected global optimal orders of convergence as well as desired superconvergence phenomena.

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Cited By

Du KFairweather GNguyen QSun W(2022)Matrix decomposition algorithms for the C 0-quadratic finite element Galerkin methodBIT10.1007/s10543-009-0233-049:3(509-526)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1007/s10543-009-0233-0
Bialecki BFairweather GKarageorghis ANguyen Q(2022)Optimal superconvergent one step quadratic spline collocation methods BIT10.1007/s10543-008-0188-648:3(449-472)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1007/s10543-008-0188-6
Bialecki BFairweather GKarageorghis AMaack J(2019)A quadratic spline collocation method for the Dirichlet biharmonic problemNumerical Algorithms10.1007/s11075-019-00676-z83:1(165-199)Online publication date: 19-Feb-2019
https://dl.acm.org/doi/10.1007/s11075-019-00676-z
Show More Cited By

Index Terms

Optimal Superconvergent One Step Nodal Cubic Spline Collocation Methods
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
    2. Numerical analysis
  2. Probability and statistics
    1. Probabilistic representations
2. Theory of computation

Index terms have been assigned to the content through auto-classification.

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cover image SIAM Journal on Scientific Computing

SIAM Journal on Scientific Computing Volume 27, Issue 2

2005

371 pages

ISSN:1064-8275

Issue’s Table of Contents

Copyright © 2005 Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2005

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Cited By

Du KFairweather GNguyen QSun W(2022)Matrix decomposition algorithms for the C 0-quadratic finite element Galerkin methodBIT10.1007/s10543-009-0233-049:3(509-526)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1007/s10543-009-0233-0
Bialecki BFairweather GKarageorghis ANguyen Q(2022)Optimal superconvergent one step quadratic spline collocation methods BIT10.1007/s10543-008-0188-648:3(449-472)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1007/s10543-008-0188-6
Bialecki BFairweather GKarageorghis AMaack J(2019)A quadratic spline collocation method for the Dirichlet biharmonic problemNumerical Algorithms10.1007/s11075-019-00676-z83:1(165-199)Online publication date: 19-Feb-2019
https://dl.acm.org/doi/10.1007/s11075-019-00676-z
Bialecki BKarageorghis A(2013)Modified nodal cubic spline collocation for three-dimensional variable coefficient second order partial differential equationsNumerical Algorithms10.1007/s11075-012-9669-464:2(349-383)Online publication date: 1-Oct-2013
https://dl.acm.org/doi/10.1007/s11075-012-9669-4
Fairweather GKarageorghis AMaack J(2011)Compact optimal quadratic spline collocation methods for the Helmholtz equationJournal of Computational Physics10.1016/j.jcp.2010.12.041230:8(2880-2895)Online publication date: 1-Apr-2011
https://dl.acm.org/doi/10.1016/j.jcp.2010.12.041
Bialecki BFairweather GKarageorghis A(2011)Matrix decomposition algorithms for elliptic boundary value problemsNumerical Algorithms10.1007/s11075-010-9384-y56:2(253-295)Online publication date: 1-Feb-2011
https://dl.acm.org/doi/10.1007/s11075-010-9384-y

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