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Error bounds for the Liouville–Green (or WKB) approximation

Published online by Cambridge University Press:  24 October 2008

F. W. J. Olver
F. W. J. Olver
Affiliation:
National Physical LaboratoryTeddingtonMiddlesex
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Abstract

Error bounds are derived and examined for approximate solutions in terms of elementary functions of the differential equations

in which u is a positive parameter, the functions f and p are free from singularities and p does not vanish. Bounds are also obtained for the remainder terms in the asymptotic expansions of the solutions in descending powers of u. The variable x ranges over a real interval, finite or infinite or over a region of the complex plane, bounded or unbounded.

Applications are made to parabolic cylinder functions of large orders, and modified Bessel functions of large orders.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 4 , October 1961 , pp. 790 - 810
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

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