KESİRLİ MERTEBEDEN PSEUDO-HİPERBOLİK KISMİ DİFERANSİYEL DENKLEMİNİN HOMOTOPİ PERTÜRBASYON YÖNTEMİYLE YAKLAŞIK ÇÖZÜMÜ

Öz

Bu çalışmada başlangıç değerlere bağlı kesirli mertebeden (Fractional order) Pseudo-Hiperbolik kısmi diferansiyel denkleminin homotopi pertürbasyon metoduyla çözümü incelenecektir. Kesirli mertebeden Pseoudo-Hiperbolik kısmi diferansiyel denkleminin farklı yöntemlerle çözümü mevcut olmasına rağmen homotopi pertürbasyon yöntemiyle çözümü daha kısa ve hata payı daha az olduğundan çözüm bu yöntemle yapılmıştır. Ayrıca Matlab programı yardımıyla tam çözüm grafik ile görselleştirilmiştir.

Anahtar Kelimeler

• Kesirli mertebe
• Pseoudo-Hiperbolik denklem
• homotopi p pertürbasyon metodu
• Tam çözüm
• Yaklaşık çözüm

APROXIMATE SOLUTION OF FRACTIONAL-ORDER PSEUDO-HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION BY HOMOTOPY PERTURBATION METHOD

Abstract

In this study, the solution of Fractional order Pseudo-Hyperbolic partial differential equation with initial conditions will be examined by homotopy perturbation method. Although the fractional Pseoudo-Hyperbolic partial differential equation has a solution with different methods, the solution is made with this method, since its solution is shorter and the margin of error is less with the homotopy perturbation method. In addition, with the help of Matlab program, the full solution was visualized with graphics.

Keywords

• Fractional order
• Pseudo-Hyperbolic equation
• homotopy p perturbation method
• Exact solution
• Approximate solution

Kaynakça

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