KdV DENKLEMİ İÇİN KUİNTİK B-SPLİNE GALERKİN METODU

Yıl 2017, Cilt: 5 Sayı: 2, 111 - 119, 31.10.2017

Dursun Irk

https://doi.org/10.20290/aubtdb.289203

Cited By: 4

Öz

Korteweg de Vries (KdV)
denklemi, Crank Nicolson parçalanması ile birlikte kuintik B-spline şekil ve
taban fonksiyonlarının kullanıldığı Galerkin sonlu elemanlar metoduyla yaklaşık
olarak çözülmüştür. Bir solitonun yayılması ve iki solitonun çarpışmasını içeren
iki klasik test problemi kullanılarak önerilen yöntemin doğruluğu kontrol
edilmiştir.  Sonuç olarak önerilen
yaklaşık yöntemin KdV denkleminin sayısal çözümü için faydalı bir yöntem olduğu
görülmüştür.

Anahtar Kelimeler

Soliton, B-spline

QUINTIC B-SPLINE GALERKIN METHOD FOR THE KdV EQUATION

Öz

The Korteweg de Vries (KdV)
equation is solved numerically based on Crank Nicolson discretization and Galerkin
finite element method using quintic B-splines as weight and element shape
functions. Two classical test problems, including propagation of a single soliton and interaction of two solitons,
are used to validate the proposed method. Finally, we conclude that the proposed
numerical method is a useful approach for numerical solution of KdV equation.

Anahtar Kelimeler

Soliton, B-spline

Kaynakça

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