The rational iteration method by Georges Lemaître

Authors
• 1 Université de Bourgogne, Institut de Mathématiques de Bourgogne, Dijon cedex, France , Dijon cedex (France)
Type
Published Article
Journal
Numerical Algorithms
Publisher
Springer US
Publication Date
May 28, 2018
Volume
80
Issue
1
Pages
235–251
Identifiers
DOI: 10.1007/s11075-018-0551-x
Source
Springer Nature
Keywords
License
Yellow

Abstract

We explain in this article how the famous Belgian astronomer and physicist Georges Lemaître, a specialist in the theory of relativity, rediscovered, during the Second World War from Gauss’ work, Aitken’s Δ2 process. He called his discovery the rational iteration method and used it to solve an ordinary differential equation. After giving some historical elements on Aitken’s Δ2 process and Steffensen’s method, we examine in detail the genesis of the rational iteration, and then its application by Lemaître to Picard’s iterates to solve the differential equation y′=dy/dx=2y2(y−x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$y^{\prime }=dy/dx= 2y^{2}(y-x)$\end{document}.

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