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On the Sturm-Liouville equation with two-point boundary conditions

Published online by Cambridge University Press:  24 October 2008

A. S. Douglas
A. S. Douglas
Affiliation:
Computer LaboratoryUniversity of Illinois*
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Abstract

In numerical solution of a Sturm-Liouville system, it is necessary to determine an eigenvalue by a method of successive approximation. A relation is derived between the estimated accuracy of an approximate eigenvalue and the accuracy at every point of its corresponding eigenfunction. A method is also described whereby the correction to a trial eigenvalue, required for convergence to its true value, can be automatically determined. This method has been successfully used in solving radial wave-function equations, both with and without ‘exchange’, arising from the Hartree-Slater-Fock analysis of Schrödinger's equation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 4 , October 1956 , pp. 636 - 639
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

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