Scaling Limit of Successive Approximations for w′=-w2

Tetsuya Hattori, Hiroyuki Ochiai

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We prove existence of scaling limits of sequences of functions defined by the recursion relation w′n+1(ϰ)= -wn(ϰ)2. which is a successive approximation to w′(ϰ)= -wn(ϰ)2 a simplest non-linear ordinary differential equation whose solutions have moving singularities. Namely, the sequence approaches the exact solution as n→ √ in an asymptotically conformal way, [formula omitted], for a sequence of numbers {qn} and a function [formula omitted]. We also discuss implication of the results in terms of random sequential bisections of a rod.

Original languageEnglish
Pages (from-to)291-319
Number of pages29
JournalFunkcialaj Ekvacioj
Volume49
Issue number2
DOIs
Publication statusPublished - 2006 Jan 1
Externally publishedYes

Fingerprint

Scaling Limit
Successive Approximation
Recursion Relations
Bisection
Nonlinear Ordinary Differential Equations
Exact Solution
Singularity

Keywords

  • Moving singularity
  • Random sequential bisections
  • Scaling limit
  • Successive approximation

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Scaling Limit of Successive Approximations for w′=-w2 . / Hattori, Tetsuya; Ochiai, Hiroyuki.

In: Funkcialaj Ekvacioj, Vol. 49, No. 2, 01.01.2006, p. 291-319.

Research output: Contribution to journalArticle

Hattori, Tetsuya ; Ochiai, Hiroyuki. / Scaling Limit of Successive Approximations for w′=-w2 In: Funkcialaj Ekvacioj. 2006 ; Vol. 49, No. 2. pp. 291-319.
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