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

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

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

Aslı Alkan(FIRAT ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ, MATEMATİK (DR))0000-0002-1036-7178
Pages
117–134
Publication Date
2022-12-29
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data:Some numerical examples are solved and compared to existing results.
💡
Conclusion & Impact: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.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Homotopi analiz metodu · Burgers denklemi · Caputo kesirli türevi

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.

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.

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Cite This Article

Alkan, A. (2022). Improving Homotopy Analysis Method with An Optimal Parameter for Time-Fractional Burgers Equation. 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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