Zaman-Kesirli Mertebeden Burgers Denklemi İçin Optimal Bir Parametre ile Homotopi Analiz Yönteminin Geliştirilmesi

Öz

Çalışmanın amacı h keyfi parametresinin seçimi ile ilgili artık hata fonksiyonunu kullanarak bu parametrenin optimal değerini belirleyerek mutlak hatayı azaltmaktır. Bazı sayısal örnekler çözülmüş ve mevcut sonuçlarla karşılaştırılmıştır. Homotopi analiz yöntemi, seri çözümler elde etmek için Burgers denklemine başarıyla uygulanmıştır. Gerekli denklemler için elde edilen çözümlere dayanarak, bu yöntemin zaman-kesirli kısmi diferansiyel denklemlere uygulanabileceği gösterilmiştir.

Anahtar Kelimeler

• Homotopi analiz metodu
• Burgers denklemi
• Caputo kesirli türevi

Improving Homotopy Analysis Method with An Optimal Parameter for Time-Fractional Burgers Equation

Öz

The aim of the study is to reduce the absolute error by determining the optimal value of this arbitrary parameter using the residual error function related to the selection of the arbitrary parameter h. Some numerical examples are solved and compared to existing results. The homotopy analysis method has been successfully implemented to Burgers equation to obtain serial solutions. On the base of the solutions obtained for the required equations, it has been shown that this method is applicable to time-fractional partial differential equations.

Anahtar Kelimeler

• Homotopy analysis method
• Burgers equation
• Caputo fractional derivative
• Homotopi analiz metodu
• Burgers denklemi
• Caputo kesirli türevi

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