Accurate calculation of the solutions to the Thomas-Fermi equations

作者：Amore Paolo; Boyd John P; Fernandez Francisco M^*

来源：Applied Mathematics and Computation, 2014, 232: 929-943.

DOI：10.1016/j.amc.2014.01.137

• Thomas-Fermi equations
• Critical slope
• Singular points
• Hankel-Pade method
• Power series
• Fade approximants
• Hermite-Pade approximants
• Chebyshev polynomials

We obtain highly accurate solutions to the Thomas-Fermi equations for atoms and atoms in very strong magnetic fields. We apply the Pade-Hankel method, numerical integration, power series with Fade and Hermite-Pade approximants and Chebyshev polynomials. Both the slope at origin and the location of the right boundary in the magnetic-field case are given with unprecedented accuracy.

• 出版日期2014-4-1