article

Stabilization of Cowell's method

Authors:

E. Stiefel,

D. G. BettisAuthors Info & Claims

Numerische Mathematik, Volume 13, Issue 2

Pages 154 - 175

https://doi.org/10.1007/BF02163234

Published: 01 May 1969 Publication History

Abstract

This paper offers a modification of the Cowell method for the integration of orbits. The modification is characterized by the property that it will integrate unperturbed Kepler motion exactly (excluding truncation errors), thus the slight instability of the Cowell Method is avoided. Furthermore, the modification takes into account the most important secular effects of orbit motion. As an example of the applicability of the modified method to perturbed motion, the equations of motion of an artificial earth satellite are integrated. In the case of elliptic initial conditions regularization by a Levi-Civita transformation was used.

References

[1]

BROUWER, D, and G.M. CLEMENCE: Methods of celestial mechanics, Chap. IV, 12 New York: Academic Press 1961.

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[2]

GAUTSCHI, W,: Numerical integration of ordinary differential equations based on trigonometric polynomials. Numer. Math. 3, 381-397 (1961).

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[3]

Interpolation and Allied Tables. London: Her Majesty's Stationery Office 1956.

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[4]

KUSTAANHEIMO, P., and E. STIEFEL: Perturbation theory of Kepler motion based on spinor regularization. Journal für die reine und angewandte Mathematik 218, 204-219 (1965).

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[5]

SALZER, H. E. : Trigonometric interpolation and predictor-corrector formulas for numerical integration. Zeitschrift für Angewandte Mathematik und Mechanik 42, 403-412 (1962).

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[6]

STIEFEL, E., M. ROSSLER, J. WALDVOGEL, and C, A. BURDET: Methods of regularization for computing orbits in celestial mechanics. NASA Contractor Report, NASA CR-769 (1967).

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[7]

SZEBEHELY, V. : Theory of orbits, the restricted problem of three bodies, Chap. III and X, 2.5. New York: Academic Press 1967.

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Shokri AMehdizadeh Khalsaraei MMohammad-Sedighi HAtashyar A(2021)Numerical simulation of second-order initial-value problems using a new class of variable coefficients and two-step semi-hybrid methodsSimulation10.1177/003754972098082497:5(347-364)Online publication date: 1-May-2021
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Khalsaraei MShokri A(2020)An explicit six-step singularly P-stable Obrechkoff method for the numerical solution of second-order oscillatory initial value problemsNumerical Algorithms10.1007/s11075-019-00784-w84:3(871-886)Online publication date: 1-Jul-2020
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Shokri AKhalsaraei MTahmourasi MGarcia-Rubio R(2019)A new family of three-stage two-step P-stable multiderivative methods with vanished phase-lag and some of its derivatives for the numerical solution of radial Schrödinger equation and IVPs with oscillating solutionsNumerical Algorithms10.1007/s11075-018-0497-z80:2(557-593)Online publication date: 1-Feb-2019
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Index Terms

Stabilization of Cowell's method
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
2. Theory of computation
  1. Design and analysis of algorithms

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Numerische Mathematik Volume 13, Issue 2

May 1969

98 pages

ISSN:0029-599X

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Springer-Verlag

Berlin, Heidelberg

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Published: 01 May 1969

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Shokri AMehdizadeh Khalsaraei MMohammad-Sedighi HAtashyar A(2021)Numerical simulation of second-order initial-value problems using a new class of variable coefficients and two-step semi-hybrid methodsSimulation10.1177/003754972098082497:5(347-364)Online publication date: 1-May-2021
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Abstract

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