The Sinc-collocation method for solving the Thomas-Fermi equation
TLDR
The Thomas-Fermi equation is solved by the Sinc-Collocation method that converges to the solution at an exponential rate and is utilized to reduce the nonlinear ordinary differential equation to some algebraic equations.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2013-01-01 and is currently open access. It has received 52 citations till now. The article focuses on the topics: Collocation method & Differential equation.read more
Citations
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Journal ArticleDOI
Intermediate Quantum Mechanics. By Hans A. Bethe. $9.00; paperback $4.95. 1964. (W. H. Benjamin, New York and Amsterdam)
Journal ArticleDOI
Neuro-heuristics for nonlinear singular Thomas-Fermi systems
Zulqurnain Sabir,Muhammad Anwaar Manzar,Muhammad Asif Zahoor Raja,Muhammad Sheraz,Abdul-Majid Wazwaz +4 more
TL;DR: A neuro-heuristic scheme is design to solve nonlinear singular second order system based on Thomas-Fermi equation using the strength of universal approximation capabilities of feedforward artificial neural networks supported with optimization power of genetic algorithms and sequential quadratic programming.
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A new heuristic computational solver for nonlinear singular Thomas–Fermi system using evolutionary optimized cubic splines
TL;DR: Results show that proposed evolutionary paradigm CSM-GASQP is an effective, alternate, accurate, and reliable stochastic numerical solver for stiff nonlinear singular Thomas–Fermi systems.
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Accurate solution of the ThomasFermi equation using the fractional order of rational Chebyshev functions
Kourosh Parand,Mehdi Delkhosh +1 more
TL;DR: The nonlinear singular ThomasFermi differential equation for neutral atoms is solved using the fractional order of rational Chebyshev orthogonal functions (FRCs) of the first kind, FTn(t,L), on a semi-infinite domain, where L is an arbitrary numerical parameter.
Journal ArticleDOI
A new numerical approach to solve Thomas–Fermi model of an atom using bio-inspired heuristics integrated with sequential quadratic programming
TL;DR: A novel bio-inspired computing approach is developed to analyze the dynamics of nonlinear singular Thomas–Fermi equation (TFE) arising in potential and charge density models of an atom by exploiting the strength of finite difference scheme for discretization and optimization through genetic algorithms (GAs) hybrid with sequential quadratic programming.
References
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Book
Advanced mathematical methods for scientists and engineers
Carl M. Bender,Steven A. Orszag +1 more
TL;DR: A self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations is given in this paper.
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