Ordinary differential equations - Equations différentielles ordinaires

المعادلة التفاضلية differential equationهي علاقة تربط بين متحول (متغير) مستقل واحد أو أكثر والدالة function المبحوث عنها التابعة لهذه المتحولات (التي يفترض أنها وحيدة التعيين) ومشتقات هذه الدالَّة بالنسبة لهذه المتحولات، التي يفترض أنها متحولات حقيقية وكذلك الدالة.

Using differential equations for modeling performance of fault tolerance in parallel applications

In this paper we present a study on the time cost added to the grid computing as a result of the use of a coordinated checkpoint / recovery fault tolerance protocol, we aim to find a mathematical model which determined the suitable time to save the checkpoints for application, to achieve a minimum finish time of parallel application in grid computing with faults and fault tolerance protocols, we have find this model by serial modeling to the goal errors, execution environment and the chosen fault tolerance protocol all that by Kolmogorov differential equations.

Numerical Treatment of Delay-Differential Equations by Using Spline Hermite Approximations

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 interpolation 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.

Numerical Solution of Non-linear System of Partial Differential Equations by Using HPM Method

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.

Numerical Simulation Stochastic of Differential Equations by Using Spline Function Approximations

In this paper, spline approximations with five collocation points are used for the numerical simulation of stochastic of differential equations(SDE). First, we have modeled continuous-valued discrete wiener process, and then numerical asymptotic stochastic stability of spline method is studied when applied to SDEs. The study shows that the method when applied to linear and nonlinear SDEs are stable and convergent. Moreover, the scheme is tested on two linear and nonlinear problems to illustrate the applicability and efficiency of the purposed method. Comparisons of our results with Euler–Maruyama method, Milstein’s method and Runge-Kutta method, it reveals that the our scheme is better than others.

Operators approaches in studying the problem on normal oscillations of system of m capillary viscous fluid

Our aim of this paper is studying the problem on normal oscillations of system of capillary viscous fluids in vessel. We prove results about the spectrum of the problem for rotating vessel and prove that the systems of root elements ( eigenelements and associated elements ) form an Abel-Lidsky basis. Also , we use some results from the theory of J-self adjoint operators in studying the spectrum of the problem for non-rotating vessel.

Studying of the solution's stability of a generalized non stationary stochastic differential equations system

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.

The study of stability of solution for non-stationary Differential Equations System With Delay

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

Large Time Behavior of Solutions to Third Order Nonlinear Differential Equations With p-Laplacian

In this paper ,we study asymptotic properties of solutions of the following third – order differential equations with -P Laplacian. In the sequel,it is assumed that all solutions of the equation are continuously extendable throughout the entire real axis. We shall prove sufficient conditions under which all global solutions

Asymptotic Behavior of Solutions of Non-linear third- Order Differential Equations

We study the asymptotic behavior of solutions of a nonlinear differential equation. Using Bihari's integral inequality, we obtain sufficient conditions for all of continuable solutions to be asymptotic.