Kombine KdV-mKdV Denkleminin Kuintik B-Splayn Diferansiyel Kuadratür Yöntemiyle Sayısal Yaklaşımlar

Year 2019, Volume: 9 Issue: 2, 386 - 403, 30.12.2019

Murat Yağmurlu , Yusuf Uçar , Ali Başhan

https://doi.org/10.37094/adyujsci.526264

Cited By: 4

Abstract

Bu makalede, kombine Korteweg-de Vries ve modifiye edilmiş Korteweg-de Vries denkleminin (kombine KdV-mKdV) sayısal yaklaşımını elde etmek için kuintik B-spline diferansiyel kuadratür yöntemi (QBDQM) uygulanmıştır. Yöntemin etkinliği ve doğruluğu, maksimum hata normu L_\infinity ve ayrık kök ortalama kare hatası L_2 hesaplanarak ölçülmüştür. Yeni elde edilen sayısal sonuçlar, yayınlanan sayısal sonuçlarla karşılaştırıldı ve karşılaştırma, yöntemin, kombine KdV-mKdV denklemini çözmek için etkili bir sayısal şema olduğunu göstermiştir. Aynı zamanda bir kararlılık analizi de yapılmıştır.

Keywords

: Kısmi diferansiyel denklemler, Diferansiyel kuadratür metod, Kombine KdV-mKdV denklemi, Kuintik B-Splaynlar, Güçlü kararlılık-koruyucu Runge-Kutta metod

Numerical Approximation of the Combined KdV-mKdV Equation via the Quintic B-Spline Differential Quadrature Method

Abstract

In this paper, quintic B-spline differential quadrature method (QBDQM) has been used to obtain the numerical approximation of the combined Korteweg-de Vries and modified Korteweg-de Vries equation (combined KdV-mKdV). The efficiency and effectiveness of the proposed method has been tested by computing the maximum error norm L_\infinity and discrete root mean square error L_2. The newly found numerical approximations have been compared to available numerical approximations and this comparison has shown that the proposed method is an efficient one for solving 

Keywords

Partial differential equations, Differential quadrature method, Combined KdV-mKdV equation, Quintic B-Splines

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