Numerical solution of modified regularized long wave equation by using cubic trigonometric B-spline functions

Abstract

In this study, the Modified Regularized Long Wave (MRLW) equation is solved numerically.  The method used for the numerical solution of MRLW equation includes the space discretization with the Galerkin finite element method based on cubic trigonometric B-spline, and also the time discretization with the Crank-Nicolson method.  We tried to obtain a more accurate method with the help of trigonometric B-spline for the numerical solution of the MRLW equation than the existing numerical methods in the first test problem.  Then, the interaction problem of the two positive solitary waves of the MRLW equation is considered, and the conservation constants are compared with the existing ones to see the correctness of the method.

Keywords

• Cubic trigonemetric B-splines,Galerkin method,modified regularized long wave equation

Değiştirilmiş düzenli uzun dalga denkleminin kübik trigonometrik B-spline fonksiyonları kullanılarak nümerik çözümü

Abstract

Bu çalışmada, Modified Regularized Long Wave (MRLW) denklemi sayısal olarak çözülmüştür.  MRLW denkleminin sayısal çözümü için kullanılan yöntem, kübik trigonometrik B-spline'a dayalı Galerkin sonlu eleman yöntemi ile konum ayrıştırmasını ve ayrıca Crank-Nicolson yöntemiyle zaman ayrıştırmasını içerir.  İlk test probleminde MRLW denkleminin sayısal çözümü için trigonometrik B-spline yardımıyla mevcut sayısal metotlardan daha doğru bir yöntem elde etmeye çalıştık.  Daha sonra, MRLW denkleminin iki pozitif solitary dalganın etkileşimi problemi göz önüne alınmış ve korunum sabitleri, yöntemin doğruluğunu görmek için mevcut çalışmalarla karşılaştırılmıştır.

Keywords

• Galerkin metodu,kübik trigonometrik B-spline,Değiştirilmiş düzenli uzun dalga denklemi

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