APPLICATION OF THE METHOD OF DECOMPOSITION INTO EXPONENTIAL SERIES BASED ON THE SPECTRAL PARAMETER IN EIGENVALUE PROBLEMS

Authors

  • Baltabek Kanguzhin Al-Farabi Kazakh National University
  • Jamshid Khujakmetov Al-Farabi Kazakh National University

DOI:

https://doi.org/10.52754/16948645_2024_2(5)_10

Keywords:

Sturm-Liouville operator, spectral analysis, exponential series

Abstract

The article explores the application of exponential series based on the spectral parameter to solve eigenvalue problems of Sturm-Liouville operators. A novel approach for decomposing the characteristic determinant into exponential series is proposed, demonstrating effectiveness for computing large eigenvalues. The theoretical framework is supported by asymptotic formulas for eigenvalues and eigenfunctions. Practical methods for achieving higher computational precision are also discussed. The work is based on an extension of earlier methods and offers new perspectives for numerical analysis in mathematical physics.

References

Левитан Б.М., Саргсян И.С. Введение в спектральную теорию. Самосопряженные обыкновенные дифференциальные операторы. Москва: Наука, 1970. 672 стр.

Bondarenko N. An inverse problem for Sturm-Liouville operators on trees with partial information given on the potentials. // Math. Meth. Appl. Sci. - 2018. - Vol. 41.

Bondarenko N. Inverse problem for a differential operator on a star-shaped graph with nonlocal matching condition.

Law C., Pivovarchik V. Characteristic functions on quantum graphs // J. Phys. A: Math. Theor. 2009.

R. Carlson, V. Pivovarchik. Spectral asymptotics for quantum graphs with equal edge lengths. J. Phys. A: Math. Theor. 41 (2008) 145202, 16 pp.

V.V. Kravchenko, R.M. Porter, Spectral parameter power series for Sturm–Liouville problems. Math. Method Appl. Sci. 33, 459–468 (2010).

Berkolaiko G., Carlson R., Fulling S., Kuchment P. Quantum Graphs and Their Applications // Amer. Math. Soc. 2006.

Downloads

Published

2024-12-10

How to Cite

Kanguzhin , B., & Khujakmetov , J. (2024). APPLICATION OF THE METHOD OF DECOMPOSITION INTO EXPONENTIAL SERIES BASED ON THE SPECTRAL PARAMETER IN EIGENVALUE PROBLEMS. Journal of Osh State University. Mathematics. Physics. Technical Sciences, (2(5), 68–74. https://doi.org/10.52754/16948645_2024_2(5)_10

Issue

No. 2(5) (2024): BULLETIN OF OSH STATE UNIVERSITY MATHEMATICS. PHYSICS. TECHNOLOGY.

Section

MATHEMATICS

License

Copyright (c) 2024 Journal of Osh State University. Mathematics. Physics. Technical Sciences

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.