Computer Science – Numerical Analysis
Scientific paper
Dec 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993pasj...45..789t&link_type=abstract
PASJ: Publications of the Astronomical Society of Japan, vol. 45, no. 6, p. 789-793
Computer Science
Numerical Analysis
8
Fokker-Planck Equation, Globular Clusters, Numerical Analysis, Variational Principles, Accuracy, Eigenvalues
Scientific paper
The orbit-averaged Fokker-Planck equation in energy space is used to study the evolution of isotropic star clusters. Two self-similar solutions were obtained by using a method based on a generalized variational principle. Those two solutions (a collapse solution and a post-collapse solution), found by using the finite-difference method, have already been published. Moreover, the author and a collaborator obtained them in a previous study by using the same variational method as described in this paper. The numerical accuracy of the solutions, however, were not sufficient in the previous work. In particular, it was a problem that there were two possible collapse solutions for each adopted trial function. In the present study, it turns out that the main origin of this problem was in the choice of the trial functions. The two self-similar solutions were searched again using more flexible trial functions, i.e., piecewise-polynomials. As a result, the problem has been removed, and one definite collapse solution obtained.
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