Orthogonal spline collocation Laplace-modified and alternating-direction methods for parabolic problems on rectangles-Reference-Cited by-同舟云学术

Orthogonal spline collocation Laplace-modified and alternating-direction methods for parabolic problems on rectangles

Published:1993 Issue:202 Volume:60 Page:545-573
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Bialecki Bernard,Fernandes Ryan I.

Abstract

A complete stability and convergence analysis is given for two- and three-level, piecewise Hermite bicubic orthogonal spline collocation, Laplace-modified and alternating-direction schemes for the approximate solution of linear parabolic problems on rectangles. It is shown that the schemes are unconditionally stable and of optimal-order accuracy in space and time.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1993-60-202/S0025-5718-1993-1176704-7/S0025-5718-1993-1176704-7.pdf

Reference27 articles.

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2. B. Bialecki and X. C. Cai, 𝐻¹-error bounds for 𝐶¹ piecewise Hermite bicubic orthogonal spline collocation schemes, submitted.

3. Fast direct solvers for piecewise Hermite bicubic orthogonal spline collocation equations;Bialecki, Bernard;SIAM J. Numer. Anal.,1992

4. B. Bialecki and R. I. Fernandes, Implementation of orthogonal spline collocation Laplace-modified and alternating-direction methods for parabolic problems, in preparation.

5. Piecewise Hermite interpolation in one and two variables with applications to partial differential equations;Birkhoff, G.;Numer. Math.,1968

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