Exact Solutions and Linearization of Modified Emden Equation

Öz

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.

Anahtar Kelimeler

• Feasible algorithm
• Differential equations
• Symmetries
• Modified Emden equation

Modife Edilmiş Emden Denkleminin Tam Çözümleri ve Lineerleştirilmesi

Öz

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.

Anahtar Kelimeler

• Diferansiyel denklemler
• Elverişli Algoritma
• Simetriler
• Modife edilmiş Emden denklemi

Kaynakça

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