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Register a new userThe Study of Stability of Liner Differential Equations system with delay by Liapunov’s Second Method
دراسة استقرار حل جملة معادلات تفاضلية ذات تأخر زمني بمعاملات متغيرة باستخدام مبدأ ليبانوف الثاني
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Aِl-Baath University ورقة بحثية
Publication date
2016
fields
Mathematics
and research's language is
العربية
Created by
Shamra Editor
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في هذا البحث سنقوم بدراسة استقرار حل جملة معادلات تفاضلية ذات تأخر زمني باستخدام مبدأ ليبانوف الثاني .
In this paper we used Liapunov’s Second Method for study of stability of differential equations system with delay.
References used
Burton, T. A. and Hatvani, L.,1989-Stability theorems for non autonomous functional differential equations by Liapunov functional, Tohoku Math. J. 41, 65-104
Burton, T. A.1994-An example on the asymptotic stability for functional differential equations, Nonlinear Anal. Vol.8,No.3,365- 368
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تتضمن الرسالة أربعة فصول :
الفصل الأول : ويتضمن بعض المفاهيم والتعاريف والمبرهنات التي تتعلق بالبحث.
الفصل الثاني : دراسة استقرار جملة معادلات تفاضلية خطية لا توقفيه ذات تأخير زمني .
الفصل الثالث :دراسة استقرار حل جملة المعادلات التفاضلية الخطية
ذات تأخير زمني .
الفصل الرابع : دراسة استقرار حل المعادلات التفاضلية لا توقفية ذات تأخر زمني باستخدام نظرية النقطة الثابتة
Defining some of the essential definitions and conceptions.
Stochastic matrix.
Stability.
Approximate stability.
Approximate stability in the quadratic middle.
Formula of a system of unsettled non stationary stochastic
differential equations.
Formula of a generalized system of unsettled non- stationary
stochastic differential equations.
Foundations of a system of differential equations that divines the
partial moments of the second order.
Foundations of a system of differential equations that divines
matrices of Lyapunov's functions.
The necessary and sufficient conditions formatrisses of Lyapunov's
functions to assure the stability of the studied system's solution
approximately in the quadratic middle.
In this article, we propose a powerful method called
homotopy perturbation method (HPM) for obtaining the
analytical solutions for an non-linear system of partial
differential equations. We begin this article by apply HPM
method for an important models of linear and non-linear
partial differential equations.
In this paper , we will discuss the way of construction of lyapunov
function for some of linear stochastic difference equations
We will use the general method of constructions of lyapunov
function for stochastic difference equations and we will ob
tain a
sufficient conditions of asymptotic mean square stability of zero
solution for one of linear stochastic difference equations with
constant coefficient ,By using of some main theorems and
definitions for asymptotic mean square stability for linear
stochastic difference equations .
In this paper, spline technique with five collocation parameters for finding the
numerical solutions of delay differential equations (DDEs) is introduced. The presented
method is based on the approximating the exact solution by C4-Hermite spline
i
nterpolation and as well as five collocation points at every subinterval of DDE.The study
shows that the spline solution of purposed technique is existent and unique and has
strongly stable for some collocation parameters. Moreover, this method if applied to test
problem will be consistent, p-stable and convergent from order nine .In addition ,it
possesses unbounded region of p-stability. Numerical experiments for four examples are
given to verify the reliability and efficiency of the purposed technique. Comparisons show
that numerical results of our method are more accurate than other methods.
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