An efficient method to approximate eigenfunctions and high-index eigenvalues of regular Sturm–Liouville problems

M. Dehghan

Applied Mathematics and Computation, 2016, vol. 279, issue C, 249-257

Abstract: The computation of the eigenvalues of a Sturm–Liouville problem is a difficult task, when high-index eigenvalues are computed. In most previous methods, it can be seen that the uncertainty of the results increases as the estimated eigenvalues grow larger. This paper is to present some new methods in which, not only the error of calculating the higher eigenvalues does not grow, but it also vanishes as eigenvalues tend to infinity. Moreover, the proposed method gives good estimates of eigenfunctions corresponding to high eigenvalues.

Keywords: Sturm–Liouville equation; Eigenvalue; Eigenfunction; Highly oscillating integral; Asymptotic behavior (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:279:y:2016:i:c:p:249-257

DOI: 10.1016/j.amc.2016.01.026

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