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The Computer Journal 1967 10(1):108-111; doi:10.1093/comjnl/10.1.108
© 1967 by British Computer Society
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A new method of determining eigenvalues and eigenfunctions

J. A. T. Bye *

University of California, San Diego, USA

An analytical solution of the general eigenequation

[equation: see PDF]

where

[equation: see PDF]

is independently linear in the Y(r) and {lambda}i, and Y(x) is the eigenfunction and {lambda} is the eigenvalue, is developed. The eigenfunction is obtained as an analytic function of x, and the eigenvalue {lambda} is the ratio between successive functions in an expansion. The solution is always convergent, and can be used as a practical method of computing eigenparameters to a high degree of precision. Two examples of computer application are given in which the solutions are obtained as power series.


* University of California, San Diego, Scripps Institution of Oceanography, La Jolla, California.


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