An Application of Galerkin Method to Generalized Benjamin-Bona-Mahony-Burgers Equation

Öz

In this study, Galerkin finite element method is applied to generalized Benjamin-Bona-Mahony-Burgers (gBBM-B) equation. Quadratic B-spline functions are used as interpolation function. Stability analysis is investigated based on von Neumann theory. The performance of the proposed method is checked by two test problems with zero boundary conditions. As a result, it is observed that applied method is successful and efficient to show motions of some waves.

Anahtar Kelimeler

• Benjamin-Bona-Mahony-Burgers equation,Finite element,Galerkin method

Genelleştirilmiş Benjamin-Bona-Mahony Denklemine Galerkin Metodunun Bir Uygulaması

Öz

Bu çalışmada, genelleştirilmiş Benjamin-Bona-Mahony (gBBM-B) denklemine Galerkin sonlu elemanlar yöntemi uygulanmıştır. İnterpolasyon fonksiyonu olarak kuadratik B-spline fonksiyonlar kullanılmıştır. Von Neumann teorisine bağlı olarak kararlılık analizi incelenmiştir. Sıfır sınır şartları ile iki test problemi yardımıyla önerilen yöntemin performansı kontrol edilmiştir. Sonuç olarak, uygulanan yöntemin bazı dalga hareketlerini göstermek için başarılı ve etkili olduğu gözlenmiştir.

Anahtar Kelimeler

• Benjamin-Bona-Mahony-Burgers denklemi,Sonlu eleman,Galerkin metodu

Kaynakça

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