Computing high-index eigenvalues for the Sturm-Liouville equation with Robin boundary conditions

Khalili, Yasser; Dehghan, Mohammad

doi:10.22034/cmde.2024.60228.2566

Computing high-index eigenvalues for the Sturm-Liouville equation with Robin boundary conditions

Articles in Press

Document Type : Research Paper

Authors

Yasser Khalili ¹
Mohammad Dehghan ²

¹ Department of Basic Sciences‎, ‎Sari Agricultural Sciences and Natural Resources University‎, ‎578 Sari‎, ‎Iran.

² Department of Mathematics‎, ‎Sari Branch‎, ‎Islamic Azad University‎, ‎Sari‎, ‎Iran.

10.22034/cmde.2024.60228.2566

Abstract

The calculation of the high-indexed eigenvalues of Sturm-Liouville problems tends to be a complex job. The larger eigenvalues are estimated, the greater scaled errors we gain. In this paper, we study the Sturm-Liouville problems subject to Rubin boundary conditions in which the high-indexed eigenvalues are computed by means of an efficient method. On the contrary of previous methods, estimated errors of further eigenvalues are less than primary ones. A good illustration of the accuracy of our method can be delineated by some numerical examples.

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