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Optimal superconvergent one step quadratic spline collocation methods |
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| Authors: | B Bialecki G Fairweather A Karageorghis QN Nguyen |
| Institution: | (1) Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO 80401-1887, USA;(2) Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus;(3) Avanade Inc., 2211 Elliott Avenue, Seattle, WA 98121, USA |
| 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. AMS subject classification (2000) 65N35, 65N22 |
| Keywords: | elliptic boundary value problems quadratic spline collocation matrix decomposition algorithms fast Fourier transforms optimal global convergence rates superconvergence |
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