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Dergiler / Karamanoğlu Mehmetbey Üniversitesi Mühendislik ve Doğa Bilimleri Dergisi / 2022 / Cilt: 4 Sayı: 2

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

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

Aslı Alkan(FIRAT ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ, MATEMATİK (DR))0000-0002-1036-7178
Sayfa
117–134
Yayın Tarihi
2022-12-29
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Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Gerekli denklemler için elde edilen çözümlere dayanarak, bu yöntemin zaman-kesirli kısmi diferansiyel denklemlere uygulanabileceği gösterilmiştir.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Çalışmanın amacı h keyfi parametresinin seçimi ile ilgili artık hata fonksiyonunu kullanarak bu parametrenin optimal değerini belirleyerek mutlak hatayı azaltmaktır.
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Temel Bulgular & Veri:Bazı sayısal örnekler çözülmüş ve mevcut sonuçlarla karşılaştırılmıştır.
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Sonuç & Katkı:Gerekli denklemler için elde edilen çözümlere dayanarak, bu yöntemin zaman-kesirli kısmi diferansiyel denklemlere uygulanabileceği gösterilmiştir.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Homotopi analiz metodu · Burgers denklemi · Caputo kesirli türevi

Özet

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.

Abstract

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.

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Bu Makaleye Atıf Yap

Alkan, A. (2022). Zaman-Kesirli Mertebeden Burgers Denklemi İçin Optimal Bir Parametre ile Homotopi Analiz Yönteminin Geliştirilmesi. Karamanoğlu Mehmetbey Üniversitesi Mühendislik ve Doğa Bilimleri Dergisi, Cilt: 4 Sayı: 2, 117–134. https://doi.org/10.55213/kmujens.1206517

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