Extended Fisher-Kolmogorov Denklemini Çözmek İçin Kuartik B-Spline Diferansiyel Kuadratur Metot

Abstract

Extended Fisher-Kolmogorov (EFK) denkleminin bazı çözümleri kuartik B-spline diferansiyel quadrature metot (DQM) ile elde edildi. İkinci mertebeden ağırlık katsayıları kuartik B-spline fonksiyonlar ile direkt olarak elde edildi. Kuartik B-spline fonksiyonların dördüncü mertebeden türevleri mevcut olmadığından, dördüncü mertebeden ağırlık katsayıları matris çarpımı yaklaşımı ile elde edildi. EFK denklemi DQM ile ayrıklaştırıldıktan sonra adi diferansiyel denklem sistemi elde edildi ve kararlılığı güçlü bir şekilde koruyan Runge-Kutta metot ile zamana bağlı integre edildi. Metodun tamlığını kontrol etmek için üç adet test problemi çözüldü ve L₂ile L_∞hata normları hesaplandı.

Keywords

• Kısmi diferansiyel denklemler,Diferansiyel Quadrature Metot,Runge-Kutta metot

Quartic B-spline Differential Quadrature Method for Solving the Extended Fisher-Kolmogorov Equation

Abstract

Some numerical solutions of the extended Fisher-Kolmogorov(EFK) equation have been obtained via quartic B-spline differential quadrature method(DQM). 2^ndorder weighting coefficients are obtained directly by quartic B-splines. Since the 4^thorder derivatives of quartic B-splines do not exist, the 4^thorder weighting coefficients have been obtained by matrix multiplication approach. After the discretization of the eFK equation via DQM, ordinary differential equation systems have been obtained and strong stability preserving Runge-Kutta method has been used for time integration. To be able to control the accuracy of the method three test problems have been solved and error norms L₂and L_∞are calculated.

Keywords

• Partial Differential Equations,Differential Quadrature Method,Runge-Kutta method

References

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