Order Linear Delay Research Articles

BELL POLYNOMIAL SOLUTION OF LINEAR FREDHOLM-VOLTERRA INTEGRO DIFFERENTIAL EQUATION SYSTEMS WITH HYBRID DELAYS

In this study, the Bell collocation method is applied to solve system of high order linear delay Fredholm-Volterra integro differential under initial conditions. The numerical method is substantially dependent on the truncated Bell series, their derivatives, and collocation points. By using this method, solutions of the integral system are obtained from the Bell series. Additionally, the error analysis and residual functions are performed, and some examples are provided to indicate the availability and applicability of the method.

Exponential stability for a system of second and first order delay differential equations

Exponential stability of the second order linear delay differential equation in x and u-control ẍ(t)+a1(t)ẋ(h1(t))+a2(t)x(h2(t))+a3(t)u(h3(t))=0is studied, where indirect feedback control u̇(t)+b1(t)u(g1(t))+b2(t)x(g2(t))=0 connects u with the solution. Explicit sufficient conditions guarantee that both x and u decay exponentially.

Conditions for the Boundness of the Solution for Second Order Linear Delay Differential Equations

It is well known that a solution to a second order differential equation with roots of its characteristic equation in the right half plane is unbounded. If a delay of the right magnitude is introduced into the equation the solution is bounded. This paper investigates this phenomenon by imbedding a second order differential equation with first order delay by embedding the equation in a field of equivalent classes of quotients of polynomials in the modified differential and delay operator over the real field.

NEW OSCILLATION CRITERIA FOR FIRST ORDER LINEAR DIFFERENTIAL EQUATIONS WITH NON-MONOTONE DELAYS

<abstract> This paper is concerned with the oscillation of the first order linear delay differential equation $ x'(t)+q(t) x(\tau(t))=0 $, $ t\geq t_0 $, where $ q, \tau \in C([t_0,\infty),[0,\infty)) $, $ \tau(t)\leq t $, such that $ \underset{t \rightarrow \infty} {\lim} \tau(t)=\infty $. Several new oscillation criteria of iterative and non-iterative types are obtained. Two examples are presented to show the strength and applicability of these criteria over known ones. </abstract>

On solving fuzzy delay differential equation using bezier curves

In this article, we plan to use Bezier curves method to solve linear fuzzy delay differential equations. A Bezier curves method is presented and modified to solve fuzzy delay problems taking the advantages of the fuzzy set theory properties. The approximate solution with different degrees is compared to the exact solution to confirm that the linear fuzzy delay differential equations process is accurate and efficient. Numerical example is explained and analyzed involved first order linear fuzzy delay differential equations to demonstrate these proper features of this proposed problem.

Asymptotic Behavior and Stability in Linear Impulsive Delay Differential Equations with Periodic Coefficients

We study first order linear impulsive delay differential equations with periodic coefficients and constant delays. This study presents some new results on the asymptotic behavior and stability. Thus, a proper real root was used for a representative characteristic equation. Applications to special cases, such as linear impulsive delay differential equations with constant coefficients, were also presented. In this study, we gave three different cases (stable, asymptotic stable and unstable) in one example. The findings suggest that an equation that is in a way that characteristic equation plays a crucial role in establishing the results in this study.

Oscillation criteria for first order linear delay differential equations with several variable delays

Consider the first order linear differential equation with several variable delays of the form x′(t)+∑i=1mpi(t)x(t−τi(t))=0,t≥t0,where pi:[t0,∞)→[0,∞) and τi:[t0,∞)→(0,∞) are continuous functions, such that t−τi(t)→∞ (as t→∞) for all 1≤i≤m.Sufficient conditions are established under which some “lim inf-type” conditions for oscillation of all solutions remain valid if one replaces the lim inf by lim sup. This improves and generalizes many existing results in the literature, which is illustrated via examples.

New Oscillation Results for Third-Order Half-Linear Neutral Differential Equations

The main purpose of this paper is to obtain criteria for the oscillation of all solutions of a third-order half-linear neutral differential equation. The main result in this paper is an oscillation theorem obtained by comparing the equation under investigation to two first order linear delay differential equations. An additional result is obtained by using a Riccati transformation technique. Examples are provided to show the importance of the main results.

A necessary and sufficient condition for the oscillation of first order linear difference equations with several delay arguments

In this article, we discuss the oscillation of all solutions of a first order linear delay difference equation with several delay arguments and obtain some new oscillation criteria under more relaxed conditions. In particular, we establish a necessary and sufficient condition only based on the coefficient functions and delay arguments when the coefficient functions are non-negative. Examples and tables are given to illustrate our results.

Exact and Nonstandard Finite Difference Schemes for Coupled Linear Delay Differential Systems

In recent works, exact and nonstandard finite difference schemes for scalar first order linear delay differential equations have been proposed. The aim of the present work is to extend these previous results to systems of coupled delay differential equations X ′ ( t ) = A X ( t ) + B X ( t - τ ) , where X is a vector, and A and B are commuting real matrices, in general not simultaneously diagonalizable. Based on a constructive expression for the exact solution of the vector equation, an exact scheme is obtained, and different nonstandard numerical schemes of increasing order are proposed. Dynamic consistency properties of the new nonstandard schemes are illustrated with numerical examples, and proved for a class of methods.

Oscillation of First Order Linear Delay Differential Equation with Variable Coefficients

In this article the authors established sufficient condition for the oscillation of the first order linear delay differential equation ( * ) where is a positive constant, with several variable delays. Some interesting examples are provided to illustrate the results

English

English

Infinite integral conditions for oscilation of first order linear delay differential equations with positive and negative coefficients

This study obtains a new set of integral conditions for oscillation of nonautonomous delay differential equations with positive and negative coefficients. It is however, discovered that every solution of the equation oscillates infinitely.Keywords: Integral Condition, Oscillation, Positive and Negative Coefficients

Behavior of the solutions to third order linear autonomous delay differential equations

Behavior of the solutions to third order linear autonomous delay differential equations

Oscillation of a First Order Linear Impulsive Delay Differential Equation with Continuous and Piecewise Constant Arguments

A class of first order linear impulsive delay differential equation with continuous and piecewise constant arguments is studied. Using a connection between impulsive delay differential equations and non- impulsive delay differential equations sufficient conditions for the oscillation of the solutions are obtained.

Explicit integral criteria for the existence of positive solutions of first order linear delay equations

Explicit integral criteria for the existence of positive solutions of first order linear delay equations

Oscillation properties of higher order linear impulsive delay differential equations

Oscillation properties of higher order linear impulsive delay differential equations

Linear Fuzzy Delay Differential System: Analysis on Stability of Steady State

In this paper, a first order linear fuzzy delay differential system is proposed by using parametric form of alpha-cut representation of symmetric triangular fuzzy number. The steady state and linear stability of the system are also determined. The steady state is stable in absence of delay by Routh-Hurwitz criteria. For increasing delay we determine the positive real roots of the polynomial and developing the conditions. Several examples are considered to illustrate the stability of the steady state for the proposed system. Keywords: Delay Differential Equations; Fuzzy Differential Equations; Fuzzy Matrices. 2010 Mathematics Subject Classification: 34K36.

Solution of the delayed single degree of freedom system equation by exponential matrix method

In this paper, an exponential collocation method for the solution linear delay differential equations with constant delay is presented. The utility of this matrix based method is that it is very systematic and by writing a Maple program, any type of second order linear differential delay equation can be solved easily. The method is applied to three different types of delay equations; linear oscillator with delay (i) in the restoring force term, (ii) in the damping term, and (iii) in the acceleration term. Time response curves have been plotted for each type and the effect of the parameters of the delay terms has been shown. An error analysis based on residual function is carried out to show the accuracy of the results.

An Approximated Solutions for nth Order Linear Delay Integro-Differential Equations of Convolution Type Using B-Spline Functions and Weddle Method

The paper is devoted to solve nth order linear delay integro-differential equations of convolution type (DIDE's-CT) using collocation method with the aid of B-spline functions. A new algorithm with the aid of Matlab language is derived to treat numerically three types (retarded, neutral and mixed) of nth order linear DIDE's-CT using B-spline functions and Weddle rule for calculating the required integrals for these equations. Comparison between approximated and exact results has been given in test examples with suitable graphing for every example for solving three types of linear DIDE's-CT of different orders for conciliated the accuracy of the results of the proposed method.