Statistics – Computation
Scientific paper
Sep 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984apj...284..364l&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 284, Sept. 1, 1984, p. 364-380.
Statistics
Computation
7
Binary Stars, Computational Astrophysics, Fission, Polynomials, Stellar Evolution, Branching (Mathematics), Ellipsoids, Hydrodynamic Equations, Linear Equations, Perturbation Theory, Riemann Manifold, Systems Stability
Scientific paper
The bifurcation of compressible, nonellipsoidal figures from families of Riemann ellipsoids is governed by a certain linear equation, whose solutions are investigated. They are found to be given by polynomials in the Cartesian coordinates; in particular, the basic linear operator L acts invariantly on certain polynomial spaces VN, and solutions may be sought in VN. Since VN is finite-dimensional, the underlying system of integro-differential equations is reduced to a finite problem exactly, without the need of any spatial discretization for numerical purposes. The bifurcation problem is reduced by a perturbation expansion to a hierarchy of linear, inhomogeneous equations.
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