Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Monotone methods for the Thomas-Fermi equation


Author: J. W. Mooney
Journal: Quart. Appl. Math. 36 (1978), 305-314
MSC: Primary 80A30; Secondary 34B30
DOI: https://doi.org/10.1090/qam/508774
MathSciNet review: 508774
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Abstract: The boundary-value problem for the ionized atom case of the Thomas-Fermi equation is transformed to a certain convex nonlinear boundary-value problem. Two iterative procedures, previously developed for such problems, are constructed for the ionized atom problem. A comparative analysis of the efficiency of the iteration schemes is presented. The existence and uniqueness of a solution is established and the solution is shown to have monotonic dependence on the boundary conditions. Numerical bounds are obtained for a specific problem.


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DOI: https://doi.org/10.1090/qam/508774
Article copyright: © Copyright 1978 American Mathematical Society


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