An Effective High-Order Interval Method for Validating Existence and Uniqueness of the Solution of an IVP for an ODE

An Effective High-Order Interval Method for Validating Existence and Uniqueness of the Solution... Validated methods for initial value problems for ordinary differential equations produce bounds that are guaranteed to contain the true solution of a problem. When computing such bounds, these methods verify that a unique solution to the problem exists in the interval of integration and compute a priori bounds for the solution in this interval. A major difficulty in this verification phase is how to take as large a stepsize as possible, subject to some tolerance requirement. We propose a high-order enclosure method for proving existence and uniqueness of the solution and computing a priori bounds. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

An Effective High-Order Interval Method for Validating Existence and Uniqueness of the Solution of an IVP for an ODE

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2001 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1014798618404
Publisher site
See Article on Publisher Site

Abstract

Validated methods for initial value problems for ordinary differential equations produce bounds that are guaranteed to contain the true solution of a problem. When computing such bounds, these methods verify that a unique solution to the problem exists in the interval of integration and compute a priori bounds for the solution in this interval. A major difficulty in this verification phase is how to take as large a stepsize as possible, subject to some tolerance requirement. We propose a high-order enclosure method for proving existence and uniqueness of the solution and computing a priori bounds.

Journal

Reliable ComputingSpringer Journals

Published: Oct 3, 2004

References

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