Stable Parallel Algorithms For Two-Point Boundary Value Problems (1992)
| Venue: | SIAM J. Sci. Statist. Comput |
| Citations: | 22 - 1 self |
BibTeX
@ARTICLE{Wright92stableparallel,
author = {Stephen J. Wright},
title = {Stable Parallel Algorithms For Two-Point Boundary Value Problems},
journal = {SIAM J. Sci. Statist. Comput},
year = {1992},
volume = {13},
pages = {742--764}
}
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Abstract
. Some of the most widely used algorithms for two-point boundaryvalue ODEs, namely finite difference and collocation methods and standard multiple shooting, proceed by setting up and solving a structured system of linear equations. It is well known that the linear system can be set up efficiently in parallel; we show here that a structured orthogonal factorization technique can be used to solve this system, and hence the overall problem, in an efficient, parallel, and stable way. Key words. parallel algorithms, two-point boundaryvalue problems, error analysis and stability AMS(MOS) subject classifications. 65F05, 65G05, 65L10, 65L20, 65W05 1. Introduction. Many numerical algorithms for solving the linear two-point boundary value problem y 0 = M (t)y + q(t); t 2 [a; b]; y 2 R n ; (1) B a y(a) + B b y(b) = d; (2) have been proposed and studied over the last 30 years. Many of these methods require a structured linear algebraic system (for example, a block-tridiagonal or staircase ...
