Name: Constraint Satisfaction in Ordinary Differential Equations: Enclosing the Solution of the Initial Value Problem (en Inglés)
Price: 85590.00 CLP
Availability: InStock
Author: Micha Janssen
ISBN: 9783639118728

portada Constraint Satisfaction in Ordinary Differential Equations: Enclosing the Solution of the Initial Value Problem (en Inglés)

Formato

Libro Físico

Editorial

Vdm Verlag

Autor

Micha Janssen

Año

2009

Idioma

Inglés

N° páginas

152

Encuadernación

Tapa Blanda

ISBN13

9783639118728

Constraint Satisfaction in Ordinary Differential Equations: Enclosing the Solution of the Initial Value Problem (en Inglés)

Micha Janssen (Autor) · Vdm Verlag · Tapa Blanda

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Reseña del libro "Constraint Satisfaction in Ordinary Differential Equations: Enclosing the Solution of the Initial Value Problem (en Inglés)"

This work considers initial value problems (IVPs) for ordinary differential equations (ODEs) where some of the data is uncertain and given by intervals as is the case in many areas of science and engineering. Interval methods provide a way to approach these problems but they raise fundamental challenges in obtaining high accuracy and low computation costs. This work introduces a constraint satisfaction approach to these problems which enhances traditional interval methods with a pruning step based on a global relaxation of the ODE. The relaxation uses Hermite interpolation polynomials and enclosures of their error terms to approximate the ODE. Our work also shows how to find an evaluation time for the relaxation that minimizes its local error. Theoretical and experimental results show that the approach produces significant improvements in accuracy over the best interval methods for the same computation costs. The results also indicate that the new algorithm should be significantly faster when the ODE contains many operations.