Computation of the eigenvalues of a second-order boundary value problem with parameter dependent boundary conditions

Ayşe Kabataş; Süleyman Şengül; Ayşe Kabataş; Süleyman Şengül

doi:10.3934/math.2026250

AIMS Mathematics

2026, Volume 11, Issue 3: 6030-6049. doi: 10.3934/math.2026250

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Research article

Computation of the eigenvalues of a second-order boundary value problem with parameter dependent boundary conditions

Ayşe Kabataş ¹,
Süleyman Şengül ^{2
,
,}

1.
Department of Mathematics, Faculty of Science, Karadeniz Technical University, Trabzon 61080, Türkiye
2.
Department of Mathematics, Faculty of Arts and Sciences, Recep Tayyip Erdoğan University, Rize 53100, Türkiye

Received: 08 December 2025 Revised: 18 February 2026 Accepted: 03 March 2026 Published: 10 March 2026
MSC : 34B09, 34B30, 34L15

Our purpose in this paper was to determine the eigenvalues of the boundary value problem with separated and parameter dependent boundary conditions when the potential function is integrable and symmetric. We first provided the asymptotic estimates of the eigenvalues of the related problem. Second, we computed numerical results for the eigenvalues using the interpolating element free Galerkin method. Then, a few examples are presented to illustrate the power of the method and compare the asymptotical and numerical results for consistency and validity.
- boundary value problems,
- eigenvalues,
- asymptotic approximation,
- interpolating element free Galerkin method
Citation: Ayşe Kabataş, Süleyman Şengül. Computation of the eigenvalues of a second-order boundary value problem with parameter dependent boundary conditions[J]. AIMS Mathematics, 2026, 11(3): 6030-6049. doi: 10.3934/math.2026250

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Abstract

Our purpose in this paper was to determine the eigenvalues of the boundary value problem with separated and parameter dependent boundary conditions when the potential function is integrable and symmetric. We first provided the asymptotic estimates of the eigenvalues of the related problem. Second, we computed numerical results for the eigenvalues using the interpolating element free Galerkin method. Then, a few examples are presented to illustrate the power of the method and compare the asymptotical and numerical results for consistency and validity.

References

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