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Numerical Methods for Stiff Two-Point Boundary Value Problems

Kreiss, H.-O., Nichols, N. and Brown, D. L. (1986) Numerical Methods for Stiff Two-Point Boundary Value Problems. SIAM Journal on Numerical Analysis (SINUM), 23 (2). pp. 325-368. ISSN 0036-1429

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To link to this article DOI: 10.1137/0723023

Abstract/Summary

We consider the two-point boundary value problem for stiff systems of ordinary differential equations. For systems that can be transformed to essentially diagonally dominant form with appropriate smoothness conditions, a priori estimates are obtained. Problems with turning points can be treated with this theory, and we discuss this in detail. We give robust difference approximations and present error estimates for these schemes. In particular we give a detailed description of how to transform a general system to essentially diagonally dominant form and then stretch the independent variable so that the system will satisfy the correct smoothness conditions. Numerical examples are presented for both linear and nonlinear problems.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Meteorology
Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:27523
Uncontrolled Keywords:stiff boundary value problems, singular perturbation problems, turning points, one-sided difference approximations
Publisher:Society for Industrial and Applied Mathematics

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