Galerkin sonlu eleman metoduyla kısmi diferansiyel denklemlerin çözümleri
Küçük Resim Yok
Tarih
2007
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Niğde Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu yüksek lisans tezi dört bölümden olusmaktadır. Birinci bölümde galerkin sonlu elemanlar metodu hakkında bilgi verildi. Lineer olmayan esit genislik dalga (EW) denklemi, Burger denklemi, düzenli uzun dalga denklemi (RLW) hakkında bilgi verildi. ikinci bölümde, lineer olmayan esit genislik denklemi lineer sonlu elemanlar kullanarak Galerkin metoduyla çözüldü. Üçüncü bölümde, Burger denkleminin sayısal çözümü için bir Galerkin sonlu eleman metodu sunuldu. Dördüncü bölümde, düzenli uzun dalga denklemi, lineer sonlu yer elemanları kullanılarak Galerkin metodu ile çözüldü. Besinci bölümde, sonuç ve tartısma kısmı belirtildi. Anahtar Kelimeler : RLW denklemi, Sonlu eleman methodları, Galerkin, Burger denklemi, Esit genislik denklemi, Undular bore
This master thesis consists of four chapters. In the first chapter, a short introduction about finite element methods (FEM) was given. By giving the definition and properties of spline functions, some of the previous numerical methods about equal width wave equation, Non-linear Burger equation, the regularised long wave (RLW) equation are mentioned. In the second chapter, the non-linear equal width equation was solved by Galerkin?s method using linear finite elements. In the third chapter, A Galerkin finite element method was presented for numerical solution of Burgers? equation. In the fourth chapter, the regularised long wave equation was solved by Galerkin?s method using linear space finite elements. In the fifth chapter, conclusion and discussion were reported. Keywords: RLW equation, Finite element methods, Galerkin, Burgers? equation, equal width equation, Undular bore
This master thesis consists of four chapters. In the first chapter, a short introduction about finite element methods (FEM) was given. By giving the definition and properties of spline functions, some of the previous numerical methods about equal width wave equation, Non-linear Burger equation, the regularised long wave (RLW) equation are mentioned. In the second chapter, the non-linear equal width equation was solved by Galerkin?s method using linear finite elements. In the third chapter, A Galerkin finite element method was presented for numerical solution of Burgers? equation. In the fourth chapter, the regularised long wave equation was solved by Galerkin?s method using linear space finite elements. In the fifth chapter, conclusion and discussion were reported. Keywords: RLW equation, Finite element methods, Galerkin, Burgers? equation, equal width equation, Undular bore
Açıklama
Fen Bilimleri Enstitüsü, Matematik Ana Bilim Dalı
Anahtar Kelimeler
Matematik, Mathematics
