<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, the nonlinear Thomas-Fermi equation for neutral atoms by using the fractional order of rational Chebyshev functions of the second kind (FRC2), <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2018-0012_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><msubsup><mrow><mtext>FU</mtext></mrow><mtext>n</mtext><mi>α</mi></msubsup><mrow><mo>(</mo><mrow><mtext>t</mtext><mo>,</mo><mtext>L</mtext></mrow><mo>)</mo></mrow></math><tex-math>${\rm{FU}}_{\rm{n}}^\alpha  \left( {{\rm{t}},{\rm{L}}} \right)$</tex-math></alternatives></inline-formula> (t, L), on an unbounded domain is solved, where L is an arbitrary parameter. Boyd (<italic>Chebyshev and Fourier Spectral Methods, 2ed, 2000</italic>) has presented a method for calculating the optimal approximate amount of L and we have used the same method for calculating the amount of L. With the aid of quasilinearization and FRC2 collocation methods, the equation is converted to a sequence of linear algebraic equations. An excellent approximation solution of y(t), y′ (t), and y ′ (0) is obtained.</p></abstract>

In this paper, the nonlinear Thomas-Fermi equation for neutral atoms by using the fractional order of rational Chebyshev functions of the second kind (FRC2), FUnα(t,L)${\rm{FU}}_{\rm{n}}^\alpha  \left( {{\rm{t}},{\rm{L}}} \right)$ (t, L), on an unbounded domain is solved, where L is an arbitrary parameter. Boyd (Chebyshev and Fourier Spectral Methods, 2ed, 2000) has presented a method for calculating the optimal approximate amount of L and we have used the same method for calculating the amount of L. With the aid of quasilinearization and FRC2 collocation methods, the equation is converted to a sequence of linear algebraic equations. An excellent approximation solution of y(t), y′ (t), and y ′ (0) is obtained.

An efficient numerical method for solving nonlinear Thomas-Fermi equation

Department of Computer Sciences, Department of Cognitive Modelling, Institute for Cognitive and Brain Sciences

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"An efficient numerical method for solving nonlinear Thomas-Fermi equation"}

In this paper, the nonlinear Thomas-Fermi equation for neutral atoms by using the fractional order of rational Chebyshev functions of the second kind (FRC2),...

An efficient numerical method for solving nonlinear Thomas-Fermi equation

Published Online: Sep 10, 2018

Page range: 134 - 151

Received: Aug 24, 2017

DOI: https://doi.org/10.2478/ausm-2018-0012

Keywords
Thomas-Fermi equation, fractional order of rational Chebyshev functions, quasilinearization method, collocation method, unbounded domain

© 2018 Kourosh Parand et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

An efficient numerical method for solving nonlinear Thomas-Fermi equation

Published Online: Sep 10, 2018

Page range: 134 - 151

Received: Aug 24, 2017

DOI: https://doi.org/10.2478/ausm-2018-0012

KeywordsThomas-Fermi equation, fractional order of rational Chebyshev functions, quasilinearization method, collocation method, unbounded domain

© 2018 Kourosh Parand et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Thomas-Fermi equation, fractional order of rational Chebyshev functions, quasilinearization method, collocation method, unbounded domain