Computing the eigenvalues of a class of nonlocal Sturm-Liouville problems

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Abstract

In this paper, we shall use the regularized sampling method introduced recently to compute the eigenvalues of Sturm-Liouville problems with nonlocal conditions {(- y ″ + q (x) y = λ y, x ∈ [0, 1]; χ 0 (y) = 0, χ 1 (y) = 0,) where q ∈ L 1 and, χ 0 and χ 1 are continuous linear functionals defined by χ 0 (y) = ∫ 01 [y (t) d ψ 1 (t) + y ′ (t) d ψ 2 (t)], χ 1 (y) = ∫ 01 [y (t) d φ{symbol} 1 (t) + y ′ (t) d φ{symbol} 2 (t)], where χ 0 and χ 1 are independent, and ψ 1 ,ψ 2 , φ{symbol} 1 and φ{symbol} 2 are functions of bounded variations. Integration is in the sense of Riemann-Stieltjes. A few numerical examples will be presented to illustrate the merits of the method, and comparisons will be made with the exact eigenvalues when they are available. © 2009 Elsevier Ltd. All rights reserved.

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APA

Chanane, B. (2009). Computing the eigenvalues of a class of nonlocal Sturm-Liouville problems. Mathematical and Computer Modelling, 50(1–2), 225–232. https://doi.org/10.1016/j.mcm.2008.10.021

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