On the equivalence of discrete Sturm–Liouville problem with nonlocal boundary conditions to the algebraic eigenvalue problem

Jurij Novickij; Artūras Štikonas

doi:10.15388/LMR.A.2015.12

Articles

Jurij Novickij

Vilnius University

Artūras Štikonas

Vilnius University

http://orcid.org/0000-0002-5872-5501

Published 2015-12-23

https://doi.org/10.15388/LMR.A.2015.12

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Keywords

nonlocal boundary conditions
Sturm–Liouville problem
ﬁnite diﬀerence scheme
solvability

How to Cite

Novickij, J. and Štikonas, A. (2015) “On the equivalence of discrete Sturm–Liouville problem with nonlocal boundary conditions to the algebraic eigenvalue problem”, Lietuvos matematikos rinkinys, 56(A), pp. 66–71. doi:10.15388/LMR.A.2015.12.

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Abstract

We consider the ﬁnite diﬀerence approximation of the second order Sturm–Liouville equation with nonlocal boundary conditions (NBC). We investigate the condition when the discrete Sturm–Liouville problem can be transformed to an algebraic eigenvalue problem and denote this condition as solvability condition. The examples of the solvability for the most popular NBCs are provided.

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

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