Reducing the wrapping effect
type: Item
instance of: scholarly article
title: Reducing the wrapping effect
zbMATH Open document ID: 0840.65065
DOI: 10.1007/BF02238232
published in: Computing
publication date: 1996-06-30T00:00:00Z
review text: When solving ordinary differential equations with interval methods, the main difficulty is the wrapping effect. This phenomenon has nothing to do with precision-controlled arithmetic, it rather is caused by bounding sets in \(\mathbb{R}^n\) componentwise. For instance the optimal componentwise bounds for the set \(A := \{x \mid x \in \mathbb{R}^2,\;|x_1|+ 2|x_2|\leq 2\}\) are provided by the interval \(I := \{x \mid x \in \mathbb{R}^2\), \(-2 \leq x_1 \leq 2\), \(-1 \leq x_2 \leq 1\}\). Though \(I\) is the smallest interval containing \(A\), the transition from \(A\) to \(I\) doubles the area. This is the wrapping effect. The author considers ordinary differential equations with tolerances in the input data. He describes an algorithm which, instead of intervals, uses a larger family of sets. The algorithm exhibits a very small wrapping effect, but it can be applied only to systems with two equations.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 65L07
zbMATH DE Number: 769258
zbMATH Keywords: interval arithmetic
zbMATH Keywords: initial value problem
zbMATH Keywords: approximation of sets
zbMATH Keywords: wrapping effect
zbMATH Keywords: algorithm
author: Cristian Barbarosie
reviewed by: Herbert Fischer
MaRDI profile type: Publication
cites work: Circumscribing an Ellipsoid about the Intersection of Two Ellipsoids
cites work: Q5566070
cites work: Using Interval Methods for the Numerical Solution of ODE's
description: scientific article; zbMATH DE number 769258