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

Year 2018, Volume: 8 Issue: 2, 53 - 69, 28.12.2018

Turgut Ak

Abstract

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.

Keywords

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

Genelleştirilmiş Benjamin-Bona-Mahony Denklemine Galerkin Metodunun Bir Uygulaması

Abstract

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.

Keywords

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

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