### 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 |
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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 |

### Keywords

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

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory
- Geometry and Topology

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## Cite this

Hattori, T., & Ochiai, H. (2006). Scaling Limit of Successive Approximations for w′=-w

^{2}*Funkcialaj Ekvacioj*,*49*(2), 291-319. https://doi.org/10.1619/fesi.49.291