### Abstract

We prove existence of scaling limits of sequences of functions defined by the recursion relation w′_{n+1}(ϰ)= -w_{n}(ϰ)^{2}. which is a successive approximation to w′(ϰ)= -w_{n}(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 language | English |
---|---|

Pages (from-to) | 291-319 |

Number of pages | 29 |

Journal | Funkcialaj Ekvacioj |

Volume | 49 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2006 Jan 1 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory
- Geometry and Topology

### Cite this

^{2}

*Funkcialaj Ekvacioj*,

*49*(2), 291-319. https://doi.org/10.1619/fesi.49.291

**Scaling Limit of Successive Approximations for w′=-w ^{2} .** / Hattori, Tetsuya; Ochiai, Hiroyuki.

Research output: Contribution to journal › Article

^{2}',

*Funkcialaj Ekvacioj*, vol. 49, no. 2, pp. 291-319. https://doi.org/10.1619/fesi.49.291

^{2}Funkcialaj Ekvacioj. 2006 Jan 1;49(2):291-319. https://doi.org/10.1619/fesi.49.291

}

TY - JOUR

T1 - Scaling Limit of Successive Approximations for w′=-w2

AU - Hattori, Tetsuya

AU - Ochiai, Hiroyuki

PY - 2006/1/1

Y1 - 2006/1/1

N2 - 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.

AB - 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.

KW - Moving singularity

KW - Random sequential bisections

KW - Scaling limit

KW - Successive approximation

UR - http://www.scopus.com/inward/record.url?scp=85010181470&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85010181470&partnerID=8YFLogxK

U2 - 10.1619/fesi.49.291

DO - 10.1619/fesi.49.291

M3 - Article

AN - SCOPUS:85010181470

VL - 49

SP - 291

EP - 319

JO - Funkcialaj Ekvacioj

JF - Funkcialaj Ekvacioj

SN - 0532-8721

IS - 2

ER -