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Journals / AURUM Mühendislik Sistemleri ve Mimarlık Dergisi / 2020 / Cilt: 4 Sayı: 2

Exact Solutions and Linearization of Modified Emden Equation

Modife Edilmiş Emden Denkleminin Tam Çözümleri ve Lineerleştirilmesi

Özlem Orhan(BANDIRMA ONYEDI EYLUL UNIVERSITY)0000-0003-0058-0431
Bahar Milani(BANDIRMA ONYEDI EYLUL UNIVERSITY)0000-0002-5295-4215
Muhammed Milani(BANDIRMA ONYEDI EYLUL UNIVERSITY)0000-0003-2450-0280
Pages
273–282
Publication Date
2020-12-30
DOI
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AI Summary & Key Takeaways

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

Finally, all graphics of solutions have been presented with Mathematica and Matlab.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we present that the modified Emden equation has invariant solutions for arbitrary coefficients α and β.
📊
Key Findings & Data:Firstly, we demonstrated that modified Emden equation can be linearized.
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Conclusion & Impact:Finally, all graphics of solutions have been presented with Mathematica and Matlab.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Diferansiyel denklemler · Elverişli Algoritma · Simetriler

Abstract

In this study, we present that the modified Emden equation has invariant solutions for arbitrary coefficients α and β. Firstly, we demonstrated that modified Emden equation can be linearized. The symmetries of the equation can be derived using a feasible algorithm after this equation is linearized. The exact solutions of the equation are found using a new algorithm and with helping these symmetries. Additionally, finding solutions are classified with respect to the physical meaning of arbitrary coefficients. Finally, all graphics of solutions have been presented with Mathematica and Matlab.

Özet

Bu çalışmada, keyfi α ve β katsayılarını içeren modife edilmiş Emden denklemi ele alınmıştır. Öncelikle, modife edilmiş Emden denkleminin lineerleştirilebildiği gösterilmiştir. Bu denklemi lineerleştirdikten sonra, elverişli bir algoritma kullanılarak denklemin simetrileri elde edilmiştir. Bu elde edilen simetriler ve yeni algoritma kullanılarak modife edilmiş Emden denkleminin kesin çözümleri bulunmuştur. Ek olarak, bulunan çözümler içerdikleri keyfi kaysayıların fiziksel anlamlarına göre sınıflandırılmıştır. Son olarak, bulunan çözümler kullanılarak bu çözümlerin zamana göre grafikleri Mathematica ve Matlab programları ile elde edilmiştir.

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Cite This Article

Orhan, Ö., Milani, B., Milani, M. (2020). Exact Solutions and Linearization of Modified Emden Equation. AURUM Mühendislik Sistemleri ve Mimarlık Dergisi, Cilt: 4 Sayı: 2, 273–282. https://ajindex.com/articles/1456443

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