A Study of the Eigenfunctions of the Singular Sturm-Liouville Problem Using the Analytical Method and the Decomposition Technique

Basit Öğe Kaydı
dc.contributor.authorMukhtarov, Oktay Sh
dc.contributor.authorYücel, Merve
dc.date.accessioned2021-11-01T15:05:10Z
dc.date.available2021-11-01T15:05:10Z
dc.date.issued2020
dc.department[Belirlenecek]
dc.description.abstractAbstract: The history of boundary value problems for differential equations starts with the well-known studies of D. Bernoulli, J. D’Alambert, C. Sturm, J. Liouville, L. Euler, G. Birkhoff and V. Steklov. The greatest success in spectral theory of ordinary differential operators has been achieved for Sturm–Liouville problems. The Sturm–Liouville-type boundary value problem appears in solving the many important problems of natural science. For the classical Sturm–Liouville problem, it is guaranteed that all the eigenvalues are real and simple, and the corresponding eigenfunctions forms a basis in a suitable Hilbert space. This work is aimed at computing the eigenvalues and eigenfunctions of singular two-interval Sturm–Liouville problems. The problem studied here differs from the standard Sturm–Liouville problems in that it contains additional transmission conditions at the interior point of interaction, and the eigenparameter ? appears not only in the differential equation, but also in the boundary conditions. Such boundary value transmission problems (BVTPs) are much more complicated to solve than one-interval boundary value problems ones. The major difficulty lies in the existence of eigenvalues and the corresponding eigenfunctions. It is not clear how to apply the known analytical and approximate techniques to such BVTPs. Based on the Adomian decomposition method (ADM), we present a new analytical and numerical algorithm for computing the eigenvalues and corresponding eigenfunctions. Some graphical illustrations of the eigenvalues and eigenfunctions are also presented. The obtained results demonstrate that the ADM can be adapted to find the eigenvalues and eigenfunctions not only of the classical one-interval boundary value problems (BVPs) but also of a singular two-interval BVTPs.
dc.identifier.doi10.3390/math8030415
dc.identifier.issn2227-7390
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-85082404864
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.3390/math8030415
dc.identifier.urihttps://hdl.handle.net/11491/7149
dc.identifier.volume8en_US
dc.identifier.wosWOS:000524085900114
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorYücel, Merve
dc.language.isoen
dc.publisherMdpi
dc.relation.ispartofMathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjecttwo-interval problemsen_US
dc.subjectSturm-Liouville equationen_US
dc.subjecttransmission conditionsen_US
dc.subjecteigenvaluesen_US
dc.subjecteigenfunctionsen_US
dc.subjectadomian decomposition methoden_US
dc.titleA Study of the Eigenfunctions of the Singular Sturm-Liouville Problem Using the Analytical Method and the Decomposition Technique
dc.typeArticle

Dosyalar

Orijinal paket
Listeleniyor 1 - 1 / 1
Küçük Resim
İsim:
merve-yucel2020.pdf
Boyut:
335.13 KB
Biçim:
Adobe Portable Document Format
Açıklama:
Tam Metin / Full Text
İndir

Koleksiyon

WoS İndeksli Yayınlar Koleksiyonu
Makale Koleksiyonu
Scopus İndeksli Yayınlar Koleksiyonu