Global, rigorous and realistic bounds for the solution of dissipative differential equations. I: Theory
type: Item
instance of: scholarly article
title: Global, rigorous and realistic bounds for the solution of dissipative differential equations. I: Theory
zbMATH Open document ID: 0809.65077
DOI: 10.1007/BF02276880
author: Arnold Neumaier
author: Murray Hill
published in: Computing
publication date: 1994-09-01T00:00:00Z
review text: The paper deals with global, rigorous and realistic bounds for the solutions of initial value problem for dissipative differential equations. The authors use one-sided Lipschitz conditions to obtain the local and global errors. A new existence theorem is proved giving conditions under which an initial value problem has a solution that remains close to a given approximation. By methods of interval analysis, logarithmic norms and differential inequalities a set of sufficient conditions is presented that give global bounds for all times.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 627655
zbMATH Keywords: error bounds
zbMATH Keywords: dissipative differential equations
zbMATH Keywords: interval analysis
zbMATH Keywords: logarithmic norms
zbMATH Keywords: differential inequalities
reviewed by: Angel B. Dishliev
MaRDI profile type: Publication
cites work: Q5533446
cites work: Q3256529
cites work: Q3925093
cites work: Q5330830
cites work: A basic theorem in the computation of ellipsoidal error bounds
cites work: On the stability of semi-implicit methods for ordinary differential equations
cites work: Interval Slopes for Rational Functions and Associated Centered Forms
cites work: Q5594866
cites work: Interval Methods for Systems of Equations
cites work: Norm bounds for rational matrix functions
cites work: A New Modified Cholesky Factorization
cites work: On Logarithmic Norms
description: scientific article; zbMATH DE number 627655