An efficient numerical method for solving nonlinear Thomas-Fermi equation
| Autor: | Kourosh Parand, Kobra Rabiei, Mehdi Delkhosh |
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| Rok vydání: | 2018 |
| Předmět: |
34b40
fractional order of rational chebyshev functions quasilinearization method General Mathematics Numerical analysis 34b16 65n35 010103 numerical & computational mathematics 01 natural sciences Nonlinear system collocation method thomas-fermi equation 0103 physical sciences QA1-939 Applied mathematics 0101 mathematics unbounded domain 010306 general physics Mathematics Fermi Gamma-ray Space Telescope |
| Zdroj: | Acta Universitatis Sapientiae: Mathematica, Vol 10, Iss 1, Pp 134-151 (2018) |
| ISSN: | 2066-7752 2018-0012 |
| Popis: | 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), FU n α ( 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. |
| Databáze: | OpenAIRE |
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