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

Gartland, Eugene C.

doi:10.1090/S0025-5718-1984-0736445-9

Accurate approximation of eigenvalues and zeros of selected eigenfunctions of regular Sturm-Liouville problems
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by Eugene C. Gartland PDF

Math. Comp. 42 (1984), 427-439 Request permission

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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