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Solution of Extraordinary Differential Equations with Physical Reasoning by Obtaining Modal Reaction Series
المؤلف
المصدر
Modelling and Simulation in Engineering
العدد
المجلد 2010، العدد 2010 (31 ديسمبر/كانون الأول 2010)، ص ص. 1-19، 19ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2010-05-27
دولة النشر
مصر
عدد الصفحات
19
التخصصات الرئيسية
الملخص EN
Mathematical modeling of many engineering and physics problem leads to extraordinary differential equations like Nonlinear, Delayed, and Fractional Order.
An effective method is required to analyze the mathematical model which provides solutions conforming to physical reality.
A Fractional Differential Equation (FDE), where the leading differential operator is Riemann-Liouvelli (RL) type requires fractional order initial states which are sometimes hard to physically relate.
Therefore, we must be able to solve these extraordinary systems, in space, time, frequency, area, volume, with physical reality conserved.
Extra Ordinary Differential equation Systems and its solution, with Physical Principle, of action-reaction and equivalent mathematical decomposition method, are obtained as an aid for Physicists and Engineers to tackle the process dynamics with ease.
This reactions-chain generates internal modes from zeroth mode reaction to first mode second mode and to infinite modes; instantaneously in parallel time or space-scales; and the sum of all these modes gives entire system reaction.
This modal reaction as explained by physics theory exactly matches the principle of Adomian Decomposition Method (ADM).
Fractional Differential Equation (FDE) with Riemann-Liouvelli formulation linear and non-linear is solved as per ADM.
In this formulation of FDE by RL method it is found that there is no need to worry about the fractional initial states; instead one can use integer order initial states (the conventional ones) to arrive at solution of FDE.
This new finding too is highlighted in this paper-along with several other problems to give physical insight to the solution of extraordinary differential equation systems.
This way one gets insight to Physics of General Differential Equation Systems-and its solution-by Physical Principle and equivalent mathematical decomposition method.
This facilitates ease in modeling.
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Das, Shantanu. 2010. Solution of Extraordinary Differential Equations with Physical Reasoning by Obtaining Modal Reaction Series. Modelling and Simulation in Engineering،Vol. 2010, no. 2010, pp.1-19.
https://search.emarefa.net/detail/BIM-494878
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Das, Shantanu. Solution of Extraordinary Differential Equations with Physical Reasoning by Obtaining Modal Reaction Series. Modelling and Simulation in Engineering No. 2010 (2010), pp.1-19.
https://search.emarefa.net/detail/BIM-494878
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Das, Shantanu. Solution of Extraordinary Differential Equations with Physical Reasoning by Obtaining Modal Reaction Series. Modelling and Simulation in Engineering. 2010. Vol. 2010, no. 2010, pp.1-19.
https://search.emarefa.net/detail/BIM-494878
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-494878
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