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A hybrid augmented compact finite volume method for the Thomas–Fermi equation

Author

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  • Zhao, Tengjin
  • Zhang, Zhiyue
  • Wang, Tongke

Abstract

A new efficient method that combines the Puiseux series asymptotic technique with an augmented compact finite volume method is proposed to develop a numerical approximate solution for the Thomas–Fermi equation on semi-infinity domain. By using the asymptotic series of solution at infinity and the Puiseux series expansion at origin to characterize the singularities, the natural and precise boundary conditions are obtained. The expansions contain undetermined parameters which associate with the singularity as the augmented variables. A regular boundary value problem is derived, for which an augmented compact finite volume method is used. The computational results show that the method not only obtains the high precise numerical solution, but also obtains the high precise initial slope. In particular, we find that the initial slope is exactly equal to the augmented variable related to the singularities in the Puiseux series. The initial slope not only has an important physical significance, but also its calculation accuracy has become an important criteria to measure the quality of the algorithm.

Suggested Citation

  • Zhao, Tengjin & Zhang, Zhiyue & Wang, Tongke, 2021. "A hybrid augmented compact finite volume method for the Thomas–Fermi equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 760-773.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:760-773
    DOI: 10.1016/j.matcom.2021.06.010
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    References listed on IDEAS

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    1. Wang, Tongke & Zhang, Zhiyue, 2015. "A compact finite volume method and its extrapolation for elliptic equations with third boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 258-271.
    2. Zhao, Tengjin & Zhang, Zhiyue & Wang, Tongke, 2021. "A hybrid asymptotic and augmented compact finite volume method for nonlinear singular two point boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    3. Amore, Paolo & Boyd, John P. & Fernández, Francisco M., 2014. "Accurate calculation of the solutions to the Thomas–Fermi equations," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 929-943.
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