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Accurate approximation of eigenvalues and zeros of selected eigenfunctions of regular Sturm-Liouville problems


Author: Eugene C. Gartland
Journal: Math. Comp. 42 (1984), 427-439
MSC: Primary 65L15
DOI: https://doi.org/10.1090/S0025-5718-1984-0736445-9
MathSciNet review: 736445
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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 orginal 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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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1984-0736445-9
Keywords: Eigenvalues, zeros of eigenfunctions, Sturm-Liouville problems
Article copyright: © Copyright 1984 American Mathematical Society