Spectrum curves for a discrete Sturm–Liouville problem with one integral boundary condition
Articles
Kristina Bingelė
Vilnius University
https://orcid.org/0000-0002-8420-0477
Agnė Bankauskienė
Vilnius University
https://orcid.org/0000-0001-7650-8132
Artūras Štikonas
Vilnius University
https://orcid.org/0000-0002-5872-5501
Published 2019-09-26
https://doi.org/10.15388/NA.2019.5.5
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Keywords

Sturm–Liouville problem
finite difference sheme
nonlocal boundary condition
complex eigenvalues
spectrum curves

How to Cite

Bingelė K., Bankauskienė A. and Štikonas A. (2019) “Spectrum curves for a discrete Sturm–Liouville problem with one integral boundary condition”, Nonlinear Analysis: Modelling and Control, 24(5), pp. 755–774. doi: 10.15388/NA.2019.5.5.

Abstract

This paper presents new results on the spectrum on complex plane for discrete Sturm–Liouville problem with one integral type nonlocal boundary condition depending on three parameters: γ, ξ1 and ξ2. The integral condition is approximated by the trapezoidal rule. The dependence on parameter γ is investigated by using characteristic function method and analysing spectrum curves which gives qualitative view of the spectrum for fixed ξ= m/ n and ξ2 = m2 / n, where n is discretisation parameter. Some properties of the spectrum curves are formulated and illustrated in figures for various ξ1 and ξ2.

*The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014).

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