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CEBİRSEL KATSAYILI DİFERANSİYEL DENKLEMLERİN SPLİNE FONKSİYONU İLE ÇÖZÜMÜ

SOLUTION OF DIFFERENSIYEL EQUATIONS WITH ALGEBRAIC COEFFICIENTS BY SPLINE FUNCTIONS

Journal Name:

  • Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi

Publication Year:

  • 2005

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In general, a general solution method developed for closed solutions of homogeneous or non-homogeneous ordinary differential equations with algebraic coefficients do not always exist. The solutions under initial and boundary conditions of these kind of ordinary differential equations can be made by numerical methods when their general solutions cannot be obtained in closed forms. Shooting, finite differences, and Rayleigh-Ritz methods are examples for these methods that give numerical solutions under boundary conditions of the problem. In this study, solution of boundary value problems by Spline function approach, different from those methods, is considered; the methods applied for general solution of second order differential equation and the applied method is supported by examples.
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Abstract (Original Language): 
Genel olarak, cebirsel katsayılı homojen veya homojen olmayan adi diferansiyel denklemlerin kapalı çözümleri için geliştirilmiş genel bir çözüm yöntemi her zaman bulunamamaktadır. Bu tip adi diferansiyel denklemlerin genel çözümleri kapalı olarak elde edilemediğinde başlangıç veya sınır koşulları altındaki çözümleri sayısal yöntemler kullanılarak bulunabilir. Problemin sınır koşulları altındaki sayısal çözümlerini veren bu yöntemlere Shooting, sonlu farklar, Rayleigh-Ritz yöntemlerini örnek olarak verebiliriz. Bu çalışmada bu yöntemlerin dışında Spline fonksiyonu yaklaşımı ile sınır değer problemlerinin çözümü üzerinde durulmuş, ikinci mertebeden diferansiyel denklemin en genel hali için yöntem uygulanmış ve uygulanan yöntem örnekler ile desteklenmiştir.
FULL TEXT (PDF): 
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  • 3
55-68
  • Turkish

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