Homotopi Perturbasyon Metodunun Nötron Difuzyon Denklemine Uygulanması

Yıl 2023, , 70 - 84, 05.08.2024

Fatma Aktaş , Halide Koklu

https://doi.org/10.58688/kujs.1407648

Öz

Homotopi Pertürbasyon Yönteminin (HPM), matematikte hem doğrusal hem de doğrusal olmayan diferansiyel denklemlerin çözümünde etkili olduğu, fizik ve mühendislik alanlarındaki geniş bir uygulama yelpazesinde faydalı olduğu gösterilmiştir. Bu çalışmada, tek boyutlu zamandan bağımsız yaklaşım için nötron difüzyon denklemine Homotopi Pertürbasyon Yöntemi uygulanmıştır. Nötron difüzyon denkleminin Laplace operatörü kartezyen, küresel ve silindirik koordinatlar için dikkate alındı. Üç farklı sistem için elde edilen kritik yarıçap değerleri, ilgili malzeme parametresi B’nin tüm olası değerleri için hesaplandı. Sonuçlar nötron difüzyon denkleminin çözümünün literatürle uyumlu olduğunu göstermektedir.

Anahtar Kelimeler

Homotopi Pertürbasyon Yöntemi, nötron difüzyon denklemi, ikinci derece diferansiyel denklemler, küresel ve silindirik koordinatlar

Application of The Homotopy Perturbation Method to the Neutron Diffusion Equation

Öz

The Homotopy Perturbation Method (HPM) has been shown to be effective in solving both linear and nonlinear differential equations in mathematics, making it useful in a wide range of applications in the fields of physics and engineering. In this study, the Homotopy Perturbation Method was applied to the neutron diffusion equation for a one-dimensional time-independent approach. The Laplace operator of the neutron diffusion equation was considered for Cartesian, spherical and cylindrical coordinates. The critical radius values obtained for three different systems were calculated for all possible values of the relevant material parameter B. The results show that the solution of the neutron diffusion equation is agree with the literature.

Anahtar Kelimeler

Homotopy Perturbation Method, neutron diffusion equation, second order differential equations, spherical and cylindrical coordinates

Kaynakça

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