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

Öz

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.

Anahtar Kelimeler

• : 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

Öz

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 

Anahtar Kelimeler

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

Kaynakça

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