Parametrization of solutions to the Emden-Fowler equation and the Thomas-Fermi model of compressed atoms

DOI10.1134/S0965542520080138zbMath1455.34018OpenAlexW3092079833MaRDI QIDQ2206364

S. V. Pikulin

Publication date: 22 October 2020

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542520080138

zbMATH Keywords

Emden-Fowler equationparametric representationsingular Cauchy problemAbel equation of second kindmodel of compressed atomsmodified Painlevé testThomas-Fermi problem

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Theoretical approximation of solutions to ordinary differential equations (34A45) Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Singular nonlinear boundary value problems for ordinary differential equations (34B16) Parameter dependent boundary value problems for ordinary differential equations (34B08) Boundary value problems on infinite intervals for ordinary differential equations (34B40)

Cites Work

• Accurate solution of the Thomas-Fermi equation using the fractional order of rational Chebyshev functions
• Revisiting the Thomas-Fermi equation: accelerating rational Chebyshev series through coordinate transformations
• Generalized Thomas-Fermi equations as the Lampariello class of Emden-Fowler equations
• Traveling-wave solutions of the Kolmogorov-Petrovskii-Piskunov equation
• The Thomas-Fermi problem and solutions of the Emden-Fowler equation
• Analytical-numerical method for calculating the Thomas-Fermi potential
• The behavior of solutions to a special Abel equation of the second kind near a nodal singular point
• A Nonlinear Singular Boundary Value Problem in the Theory of Pseudoplastic Fluids
• An analytic solution to the Thomas–Fermi equation
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