Implementation of new iterative techniques for solutions of Thomas-Fermi and Emden-Fowler equations

DOI10.1016/0021-9991(80)90156-4zbMath0456.65054OpenAlexW2086150018MaRDI QIDQ1151008

Robert C. Flagg, W. L. Perry, C. D. Luning

Publication date: 1980

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9991(80)90156-4

zbMATH Keywords

positive solutionsiterative techniquesEmden-Fowler equationsThomas- Fermi equation

Mathematics Subject Classification ID

Quantum equilibrium statistical mechanics (general) (82B10) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items (9)

Solution of Emden-type problems using accurate, efficient discretisation schemes ⋮ A hybrid asymptotic and augmented compact finite volume method for nonlinear singular two point boundary value problems ⋮ Solution of a Thomas-Fermi problem using linear approximants ⋮ Iterative methods for a singular boundary-value problem ⋮ Enclosures of the solution of the Thomas-Fermi equation by monotone discretization ⋮ The Thomas-Fermi problem and solutions of the Emden-Fowler equation ⋮ The series expansion and Chebyshev collocation method for nonlinear singular two-point boundary value problems ⋮ Iterative procedures for nonlinear second order boundary value problems ⋮ Shape functions for separable solutions to cross-field diffusion problems

Cites Work

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• Some aspects of the Thomas-Fermi equation
• Evolution of a stable profile for a class of nonlinear diffusion equations. II
• On the Generalized Emden–Fowler Equation
• Iterative solution of the Hartree equations
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• An iterative technique for solution of the Thomas-Fermi equation utilizing a nonlinear eigenvalue problem
• An Iterative Technique for Obtaining Solutions of a Thomas–Fermi Equation
• Monotone methods for the Thomas-Fermi equation
• Evolution of a stable profile for a class of nonlinear diffusion equations with fixed boundaries
• A unified approach to the solution of certain classes of nonlinear boundary value problems using monotone iterations
• Thomas-Fermi Equation Solution by the Differential Analyzer
• Equations of State of Elements Based on the Generalized Fermi-Thomas Theory

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