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Accurate Approximation of Eigenvalues and Zeros of Selected Eigenfunctions of Regular Sturm-Liouville Problems

Eugene C. Gartland, Jr.
Mathematics of Computation
Vol. 42, No. 166 (Apr., 1984), pp. 427-439
DOI: 10.2307/2007594
Stable URL: http://www.jstor.org/stable/2007594
Page Count: 13
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Accurate Approximation of Eigenvalues and Zeros of Selected Eigenfunctions of Regular Sturm-Liouville Problems
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Abstract

A method for simultaneously approximating to high accuracy the corresponding eigenvalue and zeros of the $(n + 1)$st eigenfunction of a regular Sturm-Liouville eigenvalue problem is presented. It is based upon equilibrating the minimum eigenvalues of several problems on subintervals that form a partition of the original interval. The method is easily derived from classical mini-max variational principles. The equilibration is accomplished iteratively using an approximate Newton Method. Numerical results are given.

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