Anderson, D.; Desaix, M. Approximate solution of a Thomas-Fermi model equation for bulk self-gravitating stellar objects in two dimensions. (English) Zbl 1358.85003 Eur. J. Phys. 38, No. 1, Article ID 015406, 8 p. (2017). Summary: Direct variational methods are used to find simple approximate solutions of the Thomas-Fermi equations describing the properties of self-gravitating radially symmetric stellar objects both in the non-relativistic and ultra-relativistic cases. The approximate solutions are compared and shown to be in good agreement with exact and numerically obtained solutions. MSC: 85A15 Galactic and stellar structure 49S05 Variational principles of physics 49K20 Optimality conditions for problems involving partial differential equations 76Y05 Quantum hydrodynamics and relativistic hydrodynamics 85-08 Computational methods for problems pertaining to astronomy and astrophysics 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) Keywords:direct variational methods; Rayleigh-Ritz optimization procedure; Thomas-Fermi model equation; self-gravitating stellar objects; ultra-relativistic cases PDFBibTeX XMLCite \textit{D. Anderson} and \textit{M. Desaix}, Eur. J. Phys. 38, No. 1, Article ID 015406, 8 p. (2017; Zbl 1358.85003) Full Text: DOI References: [1] De S and Chakrabarty S 2015 Thomas–Fermi model for a bulk self-gravitating stellar object in two dimensions Eur. J. Phys.36 055006 · Zbl 1332.85004 [2] Parwani R R 2004 An approximate expression for the large angle period of a simple pendulum Eur. J. Phys.25 37–9 · Zbl 1162.70300 [3] Wan F Y M 1995 Introduction to the Calculus of Variations and its Applications (New York: Chapman and Hall) · Zbl 0843.49001 [4] Komzsik L 2009 Applied Calculus of Variations for Engineers (Boca Raton, FL: CRC Press/Taylor and Francis Group) · Zbl 1197.49001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.