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