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On the Derivation of a Closed-Form Expression for the Solutions of a Subclass of Generalized Abel Differential Equations
المؤلفون المشاركون
Tsiakalos, Apostolos
Nastou, Panayotis E.
Stamatiou, Yannis C.
Spirakis, Paul
المصدر
International Journal of Differential Equations
العدد
المجلد 2013، العدد 2013 (31 ديسمبر/كانون الأول 2013)، ص ص. 1-9، 9ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2013-07-08
دولة النشر
مصر
عدد الصفحات
9
التخصصات الرئيسية
الملخص EN
We investigate the properties of a general class of differential equations described by dy(t)/dt=fk+1(t)y(t)k+1+fk(t)y(t)k+⋯+f2(t)y(t)2+f1(t)y(t)+f0(t), with k>1 a positive integer and fi(t), 0≤i≤k+1, with fi(t), real functions of t.
For k=2, these equations reduce to the class of Abel differential equations of the first kind, for which a standard solution procedure is available.
However, for k>2 no general solution methodology exists, to the best of our knowledge, that can lead to their solution.
We develop a general solution methodology that for odd values of k connects the closed form solution of the differential equations with the existence of closed-form expressions for the roots of the polynomial that appears on the right-hand side of the differential equation.
Moreover, the closed-form expression (when it exists) for the polynomial roots enables the expression of the solution of the differential equation in closed form, based on the class of Hyper-Lambert functions.
However, for certain even values of k, we prove that such closed form does not exist in general, and consequently there is no closed-form expression for the solution of the differential equation through this methodology.
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Nastou, Panayotis E.& Spirakis, Paul& Stamatiou, Yannis C.& Tsiakalos, Apostolos. 2013. On the Derivation of a Closed-Form Expression for the Solutions of a Subclass of Generalized Abel Differential Equations. International Journal of Differential Equations،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-508973
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Nastou, Panayotis E.…[et al.]. On the Derivation of a Closed-Form Expression for the Solutions of a Subclass of Generalized Abel Differential Equations. International Journal of Differential Equations No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-508973
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Nastou, Panayotis E.& Spirakis, Paul& Stamatiou, Yannis C.& Tsiakalos, Apostolos. On the Derivation of a Closed-Form Expression for the Solutions of a Subclass of Generalized Abel Differential Equations. International Journal of Differential Equations. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-508973
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-508973
قاعدة معامل التأثير والاستشهادات المرجعية العربي "ارسيف Arcif"
أضخم قاعدة بيانات عربية للاستشهادات المرجعية للمجلات العلمية المحكمة الصادرة في العالم العربي
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