A rigorous ODE solver and Smale's 14th problem
type: Item
instance of: scholarly article
title: A rigorous ODE solver and Smale's 14th problem
zbMATH Open document ID: 1047.37012
author: W. Tucker
published in: Foundations of Computational Mathematics
publication date: 2002-01-01T00:00:00Z
review text: The author presents an algorithm for computing rigorous solutions for ordinary differential equations. The algorithm is broken down into two main parts: A local part, which is based on normal form theory, and a global part, which involves interval arithmetic with directed rounding and partitioning process. As an application of this algorithm, the author proves that the Lorenz equations support a robust strange attractor and that its flow admits a unique SRB measure, whose support coincides with the attractor.
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 65G30
zbMATH DE Number: 1760617
zbMATH Keywords: ODE solver
zbMATH Keywords: interval arithmetic
zbMATH Keywords: Lorenz equation
zbMATH Keywords: normal form
zbMATH Keywords: strange attractor
reviewed by: Faouzi Lakrad
describes a project that uses: PROFIL/BIAS
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1760617