2015
|
Sign up to set email alerts
|

Abstract: Judicious use of interval arithmetic, combined with careful pen and paper estimates, leads to effective strategies for computer assisted analysis of nonlinear operator equations. The method of radii polynomials is an efficient tool for bounding the smallest and largest neighborhoods on which a Newton-like operator associated with a nonlinear equation is a contraction mapping. The method has been used to study solutions of ordinary, partial, and delay differential equations such as equilibria, periodic orbits, … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

0
79
0

Year Published

2015
2015
2016
2016

Publication Types

Select...
2

Relationship

1
1

Authors

Journals

citations
Cited by 58 publications
(79 citation statements)
references
References 38 publications
(38 reference statements)
0
79
0
Order By: Relevance
“…A proof of this lemma can be found, e.g., in Yamamoto (1998), Day et al (2007) and Hungria et al (2016).…”
Section: N Then T Is a Contraction On B X (R ) And There Is A Unmentioning
confidence: 94%
See 3 more Smart Citations
“…A proof of this lemma can be found, e.g., in Yamamoto (1998), Day et al (2007) and Hungria et al (2016).…”
Section: N Then T Is a Contraction On B X (R ) And There Is A Unmentioning
confidence: 94%
“…The functional analytic setup is close to the one utilized in Hungria et al (2016) with the main difference lying in the convolution structure.…”
Section: The Zero Finding Problemmentioning
confidence: 99%
See 2 more Smart Citations
“…Our method, which builds on foundations laid in [10,11,12,13], is summarized as follows. At the center of the method is an approximate solution u num , obtained through a numerical calculation.…”
Section: ) We Note That the Two Phase Transitions From Rolls To Hexmentioning
confidence: 99%