# The rational iteration method by Georges Lemaître

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 $\Delta^2$ 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 $\Delta^2$ 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 $y^{\prime }=dy/dx= 2y^{2}(y-x)$.
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Journal articles

https://hal.archives-ouvertes.fr/hal-01803927
Contributor : Hervé Le Ferrand <>
Submitted on : Thursday, May 31, 2018 - 10:21:06 AM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM

### Citation

Hervé Le Ferrand. The rational iteration method by Georges Lemaître. Numerical Algorithms, Springer Verlag, 2018, pp.1-17. ⟨10.1007/s11075-018-0551-x⟩. ⟨hal-01803927⟩

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