Numerical integration errors in calculated tropospheric photodissociation rate coefficients

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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Symmetric Multistep Methods Revisited: II. Numerical Experiments

International Astronomical Union Colloquium ◽

10.1017/s0252921100031602 ◽

1999 ◽

Vol 173 ◽

pp. 309-314 ◽

Cited By ~ 3

Author(s):

T. Fukushima

Keyword(s):

Multistep Methods ◽

Computational Time ◽

Integration Time ◽

Implicit Methods ◽

Symmetric Methods ◽

Celestial Bodies ◽

The Stability ◽

Predictor Corrector ◽

Symmetric Multistep Methods ◽

Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

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A New AID for Interpolating and Assessing Collision Strengths and Rate Coefficients

International Astronomical Union Colloquium ◽

10.1017/s0252921100107535 ◽

1988 ◽

Vol 102 ◽

pp. 107-110

Author(s):

A. Burgess ◽

H.E. Mason ◽

J.A. Tully

Keyword(s):

Significant Loss ◽

Impact Excitation ◽

Rate Coefficients ◽

Electron Impact Excitation ◽

Graphical Display ◽

Practical Procedure ◽

Positive Ions ◽

Allowed Transition ◽

Computational Errors ◽

Existing Data

AbstractA new way of critically assessing and compacting data for electron impact excitation of positive ions is proposed. This method allows one (i) to detect possible printing and computational errors in the published tables, (ii) to interpolate and extrapolate the existing data as a function of energy or temperature, and (iii) to simplify considerably the storage and transfer of data without significant loss of information. Theoretical or experimental collision strengths Ω(E) are scaled and then plotted as functions of the colliding electron energy, the entire range of which is conveniently mapped onto the interval (0,1). For a given transition the scaled Ω can be accurately represented - usually to within a fraction of a percent - by a 5 point least squares spline. Further details are given in (2). Similar techniques enable thermally averaged collision strengths upsilon (T) to be obtained at arbitrary temperatures in the interval 0 < T < ∞. Application of the method is possible by means of an interactive program with graphical display (2). To illustrate this practical procedure we use the program to treat Ω for the optically allowed transition 2s → 2p in ArXVI.

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