A new method for solving the hyperbolic Kepler equation

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

1 Scopus Citations
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Author(s)

  • Baisheng Wu
  • Yixin Zhou
  • C. W. Lim
  • Huixiang Zhong
  • Zeyao Chen

Detail(s)

Original languageEnglish
Pages (from-to)432-438
Number of pages7
Journal / PublicationApplied Mathematical Modelling
Volume127
Online published15 Dec 2023
Publication statusPublished - Mar 2024

Abstract

This paper proposes a highly efficient method for solving the hyperbolic Kepler equation (HKE). The hyperbolic eccentric anomaly interval is divided into two parts: a finite interval and an infinite interval. For the finite interval, a piecewise Padé approximation is first used to establish an initial approximate solution of the HKE. For the infinite interval, an analytical initial approximate solution of the HKE is constructed. These initial approximations are highly accurate and can be further improved to higher accuracy with only one step of Schröder iteration. The proposed method only requires the evaluation of no more than three transcendental functions. © 2023 Elsevier Inc.

Research Area(s)

  • Hyperbolic Kepler equation, Padé approximation, Schröder iteration

Citation Format(s)

A new method for solving the hyperbolic Kepler equation. / Wu, Baisheng; Zhou, Yixin; Lim, C. W. et al.
In: Applied Mathematical Modelling, Vol. 127, 03.2024, p. 432-438.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review