共查询到20条相似文献，搜索用时 78 毫秒
1.
W. E. Haymes 《Astrophysics and Space Science》1982,84(2):307-316
The Schwartz iteration procedure is used to compute the lowest eigenvalue from the equation for radial oscillations of stars. It was found that the convergence of the iteration had an oscillating convergence. This made it unsuitable for the computation of the higher eigenvalues. A series of associated Laguerre functions is suggested as a method of obtaining better results.Formerly at the University of Manchester, England 相似文献
2.
李焱 《中国天文和天体物理学报》1989,(4)
本文发展了一种解恒星线性非绝热非径向脉动问题的退耦化方法。这个方法把非绝热非径向脉动问题的六阶线性微分方程,分解为由一个代数方程联系起来的一个四阶线性微分方程和另一个二阶线性微分方程进行数值求解。这样的一个退耦处理,有利于克服以前在数值解这类问题时常常遇到的收敛域小和收敛速度慢等困难,并且为数值解方程时所采用的Henyey方法提供了一个自然和方便的初始猜测解。 相似文献
3.
Preliminary orbit determination is a multipoint boundary value problem which may be solved by the generalized Newton-Raphson iteration. When applied formally the method suffers from extensive computer storage requirements, fairly long execution times and in some cases, insufficient accuracy. In this work we seek to remove these practical difficulties via modification of the computational algorithm in such a way that solution storage is eliminated for the most part and computational speed and tolerance to imprecise integration algorithms is improved. The modified methods are applied to nine typical preliminary orbit determination problems to demonstrate fast convergence and short computation times, even with very poor starting values for the iteration. Excellent precision of the resulting solution is also demonstrated as well as the algorithm's ability to handle circular, elliptic, parabolic and hyperbolic orbits. 相似文献
4.
Abdel-Fattah Attia 《Experimental Astronomy》2016,42(3):343-359
The paper presents an adaptive particle swarm optimization (APSO) as an alternative method to determine the optimal orbital elements of the star η Bootis of MK type G0 IV. The proposed algorithm transforms the problem of finding periodic orbits into the problem of detecting global minimizers as a function, to get a best fit of Keplerian and Phase curves. The experimental results demonstrate that the proposed approach of APSO generally more accurate than the standard particle swarm optimization (PSO) and other published optimization algorithms, in terms of solution accuracy, convergence speed and algorithm reliability. 相似文献
5.
We consider Newton’s method for computing periodic orbits of dynamical systems as fixed points on a surface of section and
seek to clarify and evaluate the method’s uncertainty of convergence. Several fixed points of various multiplicities, both
stable and unstable are computed in a new version of Hill’s problem. Newton’s method is applied with starting points chosen
randomly inside the maximum possible—for any method—circle of convergence. The employment of random starting points is continued
until one of them leads to convergence, and the process is repeated a thousand times for each fixed point. The results show
that on average convergence occurs with very few starting points and non-converging iterations being wasted. 相似文献
6.
A. M. Kasaurov 《Astrophysics》2001,44(1):121-130
The albedo-shifting method is used to solve the problem of radiative transfer at line frequencies. Radiative transfer with complete frequency redistribution in a plane-parallel, semi-infinite atmosphere is considered. It is shown that the method works well in this case and enables one to considerably improve the convergence in an iterative solution of the equation for the source function. 相似文献
7.
Electron-acoustic waves are studied with orbital angular momentum (OAM) in an unmagnetized collisionless uniform plasma, whose constituents are the Boltzmann hot electrons, inertial cold electrons and stationary ions. For this purpose, we employ the fluid equations to obtain a paraxial equation in terms of cold electron density perturbations, which admits both the Gaussian and Laguerre–Gaussian (LG) beam solutions. Furthermore, an approximate solution for the electrostatic potential problem is found, which also allows us to express the components of the electric field in terms of LG potential perturbations. Calculating the energy flux of the electron-acoustic waves, an OAM density for these waves is obtained. Numerically, it is found that the parameters, such as, azimuthal angle, radial and angular mode numbers, and the beam waist strongly modify the LG potential profiles associated with electron-acoustic waves. The present results should be helpful to study the trapping and transportation of plasma particles and energy as well as to understand the electron-acoustic mode excitations produced by the Raman backscattering of laser beams in a uniform plasma. 相似文献
8.
D. N. Papadakos 《Celestial Mechanics and Dynamical Astronomy》1983,30(3):275-282
The existence of power series, analogous to the familiarf andg series of the two-body problem, is demonstrated in the case of then-body problem, and recursive formulae are deduced for the derivation of the coefficients of these series. In addition a proof of the convergence of the power series solution of then-body problem is given, based on the developed series. 相似文献
9.
G. Q. Wu 《Astrophysics and Space Science》1992,189(2):171-180
This paper introduces a new method of solving the equation of multi-level non-LTE radiative transfer subject to constraints. This method is based on the combination of the advantages of the complete linearization method by Auer and Mihalas (1969) and the simple separated-iteration technique (Mihalas, 1978). First, linearize the equation of radiative transfer and constraints, respectively, then solve the linearized equation of the radiative transfer and linearized constraints, separately. It overcomes the disadvantages of requiring the simultaneous solution of the corresponding equations by the complete linearization method and the poor convergence of the simple separated-iteration technique. Therefore, it not only can deal with complex models, but also has a high speed of convergence in the calculation of multi-level NLTE line formation. 相似文献
10.
Carol A. Williams 《Celestial Mechanics and Dynamical Astronomy》1984,34(1-4):395-410
Small divisors caused by certain linear combinations of frequencies appear in all analytical planetary theories. With the exception of the deep resonance between Neptune and Pluto, they can be removed at the expense of introducing secular and mixed secular terms, limiting the domain in which the solution is valid. Because of them classical solutions are known not to converge uniformly; Poincaré referred to them as asymptotic. The KAM theory shows that if one is far enough from exact commensurability and has small enough planetary masses, expansions exist which will converge to quasi-periodic orbits. Solutions showing very small divisors are excluded from this region of convergence. The question of whether they are intrinsic to the problem or are just manifestations of the method of solution is not settled. Problems with a single commensurabily that can be isolated from the rest of the Hamiltonian may have solutions with no small divisors. The problem of two or more commensurabilities remains unsolved. 相似文献
11.
In this paper, we consider a statistical method for distance determination of stellar groups. The method depends on the assumption
that the members of the group scatter around a mean absolute magnitude in Gaussian distribution. The mean apparent magnitude
of the members is then expressed by frequency function, so as to correct for observational incompleteness at the faint end.
The problem reduces to the solution of a highly transcendental equation for a given magnitude parameter α. For the computational developments of the problem, continued fraction by the Top-Down algorithm was developed and applied
for the evaluation of the error function erf(z). The distance equation Λ(y) = 0 was solved by an iterative method of second order of convergence using homotopy continuation technique. This technique
does not need any prior knowledge of the initial guess, a property which avoids the critical situations between divergent
and very slow convergent solutions, that may exist in the applications of other iterative methods depending on initial guess. 相似文献
12.
According to the optimal control theory, the optimal control problem of the low-thrust tra jectory can be converted into a solution of nonlinear two- point boundary-value problem (TPBVP). To solve the TPBVP, the repeated random guesses for the initial costate variables and iterative computations are needed. In order to enhance the convergence of the iterations, we select an appropriate performance index, and then linearize the equations of the TPBVP around a Keplerian orbit. For multi-revolution transfers, instead of the multi- revolution Lambert tra jectory, multiple segmented Keplerian arcs are used to ensure the effectiveness of the linearization. The method is totally automatic with multiple iterations. With this method, we can get the results within 3 ∼ 5 iterations, and the random guess of the initial costates is unnecessary. Finally by the iterative optimization of the performance index, a better control strategy approaching to the bang-bang control is obtained. 相似文献
13.
Dagmara Oszkiewicz Karri Muinonen Jenni Virtanen Mikael Granvik 《Meteoritics & planetary science》2009,44(12):1897-1904
Abstract— We present a novel Markov‐Chain Monte‐Carlo orbital ranging method (MCMC) for poorly observed single‐apparition asteroids with two or more observations. We examine the Bayesian a posteriori probability density of the orbital elements using methods that map a volume of orbits in the orbital‐element phase space. In particular, we use the MCMC method to sample the phase space in an unbiased way. We study the speed of convergence and also the efficiency of the new method for the initial orbit computation problem. We present the results of the MCMC ranging method applied to three objects from different dynamical groups. We conclude that the method is applicable to initial orbit computation for near‐Earth, main‐belt, and transneptunian objects. 相似文献
14.
Seungheon Song C. W. Jung S. Y. Kim Youngbo Choi 《Astrophysics and Space Science》1992,193(2):217-234
TheN-body problem does not have an exact and analytic solution, and computer technique or computer simulation can be a good candidate to solve it. Computing speed in computer simulation is very important. There are many algorithms and computational methods in computer simulation which reduce computer time.In this report a computer simulation model in a cylindrical coordinate, in which the FACR (Fourier Analysis and Cyclic Reduction) method is used, has been proposed and demonstrated the presence of spiral, barred, and ringed galaxy. The method using a cylindrical grid has good symmetrical properties specially for rotating stellar systems. 相似文献
15.
G. Allen Gary 《Solar physics》1996,163(1):43-64
The potential magnetic field from a finite planar boundary is extrapolated into the upper hemisphere using information from all three magnetic field components. The method determines, first, the transverse field associated with the observed normal magnetic intensity. Then by subtraction, the method determines the associated transverse magnetic field observed in the interior (i.e., in the field of view) of the magnetogram which is due to the normal flux exterior to the field of view of the magnetogram. Inverting this information gives an approximation to the exterior normal flux. The combination of the observed normal flux of the interior and the approximation of the exterior normal flux is employed to calculate the potential field. The formulation of the problem results in an ill-posed integral inversion problem in which a regularized solution is obtained using the singular value decomposition (SVD) technique in conjunction with an appropriate Tikhonov-Phillips filter. The technique can be applied to correcting potential field calculations which are influenced by out-of-view fluxes, e.g., for a high spatial resolution vector magnetogram with a small field of view in which there is no supporting exterior data. The problem studied is also important in providing a regularized solution of the Cauchy potential problem. The method provides a much larger range of convergence than the method of Gary and Musielak (1992), and, in fact, is stable in the total upper hemisphere.The U.S. Government right to retain a non-exclusive, royalty-free licence in and to any copyright is acknowledged. 相似文献
16.
A method has been developed for computing the gravitational force field of an axially symmetric flat galaxy from its surface mass density. The method is simple to program, fast, and accurate. An inversion formula is derived that allows computation of surface density from rotation curves by use of any method that converts density to force. The method is compared with a method of Clutton-Brock that utilizes Hankel transforms of Laguerre functions. 相似文献
17.
Virendra Singh 《Celestial Mechanics and Dynamical Astronomy》1977,16(2):137-142
In this article the existence of periodic solutions in Hill's relativistic problem is demonstrated using Poincaré's small parameter method. This method guarantees the convergence of the series representing the periodic solutions. 相似文献
18.
S. B. Faruque 《Celestial Mechanics and Dynamical Astronomy》2003,87(4):353-369
A new analytic expression for the position of the infinitesimal body in the elliptic Sitnikov problem is presented. This solution is valid for small bounded oscillations in cases of moderate primary eccentricities. We first linearize the problem and obtain solution to this Hill's type equation. After that the lowest order nonlinear force is added to the problem. The final solution to the equation with nonlinear force included is obtained through first the use of a Courant and Snyder transformation followed by the Lindstedt–Poincaré perturbation method and again an application of Courant and Snyder transformation. The solution thus obtained is compared with existing solutions, and satisfactory agreement is found. 相似文献
19.
Estimates are made of the accuracy with which the brightness distributions across the disks of stars can be reconstructed
through analysis of data from high precision space-based photometry of classical eclipsing systems and observations of the
transit of planets across stellar disks. The ill-posed reconstruction problem was solved on a compact set of monotonically
nonincreasing, upwardly convex, non-negative functions. One of the difficulties with this method in the case of stars with
thin photospheres is the poor convergence of the solution at the point where the brightness distribution has a discontinuity
at the edge of the star's disk. Nevertheless, the use of this method for analysis of high precision observational data is
justified, since it can be used to obtain an estimate of the limb darkening that is independent of any model assumptions.
The reconstructed brightness distribution for the star HD 209458, for which the transit of a planet over its disk was observed
with the HST space telescope, is in good agreement with the results of a nonlinear model fit.
Translated from Astrofizika, Vol. 51, No. 4, pp. 595–606 (November 2008). 相似文献
20.
A. Habib J. Vernin Z. Benkhaldoun H. Lanteri 《Monthly notices of the Royal Astronomical Society》2006,368(3):1456-1462
In this paper, we present a new method to estimate, for each turbulent layer labelled i , the horizontal wind speed v ( h i ) , the standard deviation of the horizontal wind speed fluctuations σ v ( hi ) and the integrated value of C 2 n over the thickness Δ hi of the turbulent layer C 2 n ( hi )Δ hi , where hi is the altitude of the turbulent layer. These parameters are extracted from single star scintillation spatiotemporal cross-correlation functions of atmospheric speckles obtained within the generalized mode. This method is based on the simulated annealing algorithm to find the optimal solution required to solve the problem. Astrophysics parameters for adaptive optics are also calculated using C 2 n ( hi ) and v ( hi ) values. The results of other techniques support this new method. 相似文献