İkinci ve dördüncü dereceden Sturm-Liouville tipinde iki noktalı sınır değer problemlerinin özdeğerlerinin varyasyonel iterasyon ve homotopi pertürbasyon yöntemleriyle hesaplanması
Küçük Resim Yok
Tarih
2009
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Niğde Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Sturm-Liouville problemleri matematiğin çeşitli alanlarında, aynı zamanda mühendislik uygulamalarında (özellikle maddesel sistemlerin salınım hareketinin, telin enine salınım hareketinin,esnek çubuğun boyuna salınım hareketinin,borularda ses dalgalarının,elektrik salınım hareketinin incelenmesinde vb.) sıkça karşılaşılan ve ilgili problemin özdeğer ve özfonksiyonlarının bulunmasıyla ilgili problemlerdir. Sturm-Liouville tipindeki problemlerin özdeğer ve özfonksiyonlarının hesaplanmasıyla ilgili,Adomian Decomposition Method (ADM), İterative Shooting Method, Runga-Kutta metod, Legendre-Galerkin-Chebyshev collacation metodu, sonlu farklar vb. gibi bir çok metod vardır.Biz bu çalışmada Varyasyonel İterasyon Metod(VIM) ve Homotopy Pertürbasyon Metod(HPM) olarak adlandırılan ve son dönemde önerilmiş olan, ayrıca pek çok lineer ve lineer olmayan adi diferansiyel denkleme başarıyla uygulanmış olan bu analitik yaklaşım tekniklerini ikinci ve dördüncü dereceden Sturm-Liouville problemlerinin özdeğerlerini hesaplamada kullandık.Anahtar sözcükler: Sturm-Liouville, Sınır değer problemler, Homotopy Pertürbasyon Metod, Varyasyonelİterasyon Metod
Sturm-Liouville (S-L) type boundary value problems are encountered in many fields of mathematics, physics as well as in many applications of engineering frequently ( in oscillation of masses, lateral vibration of thin spring, longitudinal vibration of an elastic bar, wave propagation in elastic tubes etc. ) and these problems are mainly deals with finding eigenvalues and eigenfunctions of the related problem.There are many different numerical or analytical methods available in the literature to determine the eigenvalues and eigenfunctions of Sturm-Liouville type boundary value problems. Among these methods , Adomian Decomposition Method (ADM), Iterative Shooting Method, Runga-Kutta Method, Legendre-Galerkin-Chebyshev Collocation Method, Finite Differences Method (FDM), Finite Element Method (FEM), Variational Methods, Shooting Methods are foremost used ones used by researchers of this field.In this study, recently proposed two different analytical approximation solution technique Variational Iteration Method (VIM) and Homotopy Perturbation Method (HPM) , which are used frequently for finding solutions of linear and nonlinear ordinary differential equations successfully, are used to find eigenvalues of second and fourth order Sturm-Liouville boundary value problems.Key words: Sturm-Liouville, boundary value problems, Homotopy Perturbation Method ,Variaitonal Iteration Method
Sturm-Liouville (S-L) type boundary value problems are encountered in many fields of mathematics, physics as well as in many applications of engineering frequently ( in oscillation of masses, lateral vibration of thin spring, longitudinal vibration of an elastic bar, wave propagation in elastic tubes etc. ) and these problems are mainly deals with finding eigenvalues and eigenfunctions of the related problem.There are many different numerical or analytical methods available in the literature to determine the eigenvalues and eigenfunctions of Sturm-Liouville type boundary value problems. Among these methods , Adomian Decomposition Method (ADM), Iterative Shooting Method, Runga-Kutta Method, Legendre-Galerkin-Chebyshev Collocation Method, Finite Differences Method (FDM), Finite Element Method (FEM), Variational Methods, Shooting Methods are foremost used ones used by researchers of this field.In this study, recently proposed two different analytical approximation solution technique Variational Iteration Method (VIM) and Homotopy Perturbation Method (HPM) , which are used frequently for finding solutions of linear and nonlinear ordinary differential equations successfully, are used to find eigenvalues of second and fourth order Sturm-Liouville boundary value problems.Key words: Sturm-Liouville, boundary value problems, Homotopy Perturbation Method ,Variaitonal Iteration Method
Açıklama
Fen Bilimleri Enstitüsü, Matematik Ana Bilim Dalı
Anahtar Kelimeler
Matematik, Mathematics
