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Chaotic behaviour in the newton iterative function associated with Kepler's equation

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Chaotic behaviour in the newton iterative function associated with Kepler's equation. / Stumpf, L ; Kormos, Laura.
In: Celestial Mechanics and Dynamical Astronomy, Vol. 74, No. 2, 06.1999, p. 95-109.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Stumpf, L & Kormos, L 1999, 'Chaotic behaviour in the newton iterative function associated with Kepler's equation', Celestial Mechanics and Dynamical Astronomy, vol. 74, no. 2, pp. 95-109. https://doi.org/10.1023/A:1008339416143

APA

Stumpf, L., & Kormos, L. (1999). Chaotic behaviour in the newton iterative function associated with Kepler's equation. Celestial Mechanics and Dynamical Astronomy, 74(2), 95-109. https://doi.org/10.1023/A:1008339416143

Vancouver

Stumpf L, Kormos L. Chaotic behaviour in the newton iterative function associated with Kepler's equation. Celestial Mechanics and Dynamical Astronomy. 1999 Jun;74(2):95-109. doi: 10.1023/A:1008339416143

Author

Stumpf, L ; Kormos, Laura. / Chaotic behaviour in the newton iterative function associated with Kepler's equation. In: Celestial Mechanics and Dynamical Astronomy. 1999 ; Vol. 74, No. 2. pp. 95-109.

Bibtex

@article{97bf5792375a443baf93058e9ded855e,
title = "Chaotic behaviour in the newton iterative function associated with Kepler's equation",
abstract = "The chaotic behaviour observed when Newton's method is used to solve Kepler's equation is analysed using methods borrowed from chaos theory. The result of the analysis is compared with previous results. A sufficient condition for convergence of a given iterative function is presented and yields ranges of eccentricity and mean anomaly such that Newton's method applied to Kepler's equation will converge from an initial guess of pi.",
keywords = "Kepler's equation, Schwarzian derivative, Newton's method",
author = "L Stumpf and Laura Kormos",
year = "1999",
month = jun,
doi = "10.1023/A:1008339416143",
language = "English",
volume = "74",
pages = "95--109",
journal = "Celestial Mechanics and Dynamical Astronomy",
issn = "0923-2958",
publisher = "Springer Netherlands",
number = "2",

}

RIS

TY - JOUR

T1 - Chaotic behaviour in the newton iterative function associated with Kepler's equation

AU - Stumpf, L

AU - Kormos, Laura

PY - 1999/6

Y1 - 1999/6

N2 - The chaotic behaviour observed when Newton's method is used to solve Kepler's equation is analysed using methods borrowed from chaos theory. The result of the analysis is compared with previous results. A sufficient condition for convergence of a given iterative function is presented and yields ranges of eccentricity and mean anomaly such that Newton's method applied to Kepler's equation will converge from an initial guess of pi.

AB - The chaotic behaviour observed when Newton's method is used to solve Kepler's equation is analysed using methods borrowed from chaos theory. The result of the analysis is compared with previous results. A sufficient condition for convergence of a given iterative function is presented and yields ranges of eccentricity and mean anomaly such that Newton's method applied to Kepler's equation will converge from an initial guess of pi.

KW - Kepler's equation

KW - Schwarzian derivative

KW - Newton's method

U2 - 10.1023/A:1008339416143

DO - 10.1023/A:1008339416143

M3 - Journal article

VL - 74

SP - 95

EP - 109

JO - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

SN - 0923-2958

IS - 2

ER -