KdV DENKLEMİ İÇİN KUİNTİK B-SPLİNE GALERKİN METODU

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

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.

Keywords:

Soliton, B-spline,

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