scholarly journals Integration Processes of Delay Differential Equation Based on Modified Laguerre Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Yeguo Sun
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Numerical Integration ◽  
Delay Differential Equations ◽  
Weighted Sobolev Space ◽  
Laguerre Functions ◽  
Integration Process ◽  
Spectral Accuracy ◽  
Long Time ◽  
Delay Differential

We propose long-time convergent numerical integration processes for delay differential equations. We first construct an integration process based on modified Laguerre functions. Then we establish its global convergence in certain weighted Sobolev space. The proposed numerical integration processes can also be used for systems of delay differential equations. We also developed a technique for refinement of modified Laguerre-Radau interpolations. Lastly, numerical results demonstrate the spectral accuracy of the proposed method and coincide well with analysis.

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

scholarly journals Oscillation Criteria for Second Order Neutral Differential Equations

1996 ◽  
Vol 48 (4) ◽  
pp. 871-886 ◽  
Author(s):  
Horng-Jaan Li ◽  
Wei-Ling Liu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Image Position ◽  
Delay Differential

AbstractSome oscillation criteria are given for the second order neutral delay differential equationwhere τ and σ are nonnegative constants, . These results generalize and improve some known results about both neutral and delay differential equations.

Oscillations of Neutral Delay Differential Equations

1986 ◽  
Vol 29 (4) ◽  
pp. 438-445 ◽  
Author(s):  
G. Ladas ◽  
Y. G. Sficas
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Delay Differential Equation ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

AbstractThe oscillatory behavior of the solutions of the neutral delay differential equationwhere p, τ, and a are positive constants and Q ∊ C([t0, ∞), ℝ+), are studied.

scholarly journals Approximate Solutions of Delay Differential Equations with Constant and Variable Coefficients by the Enhanced Multistage Homotopy Perturbation Method

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
D. Olvera ◽  
A. Elías-Zúñiga ◽  
L. N. López de Lacalle ◽  
C. A. Rodríguez
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Numerical Integration ◽  
Delay Differential Equations ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
Integration Algorithm ◽  
Homotopy Perturbation ◽  
Delay Differential

We expand the application of the enhanced multistage homotopy perturbation method (EMHPM) to solve delay differential equations (DDEs) with constant and variable coefficients. This EMHPM is based on a sequence of subintervals that provide approximate solutions that require less CPU time than those computed from the dde23 MATLAB numerical integration algorithm solutions. To address the accuracy of our proposed approach, we examine the solutions of several DDEs having constant and variable coefficients, finding predictions with a good match relative to the corresponding numerical integration solutions.

MULTI-SCALE DYNAMICS IN STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH MULTIPLICATIVE NOISE

2005 ◽  
Vol 05 (02) ◽  
pp. 233-246 ◽  
Author(s):  
R. KUSKE
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Nonlinear Models ◽  
Stochastic Delay Differential Equations ◽  
Oscillatory Solutions ◽  
Stochastic Delay ◽  
Multi Scale ◽  
Long Time ◽  
Parametric Noise ◽  
Delay Differential

We apply multi-scale analysis to stochastic delay-differential equations with multiplicative or parametric noise, deriving approximate stochastic equations for the amplitudes of oscillatory solutions near critical delays. Reduced equations for the envelope of the oscillations provides an efficient analysis of the dynamics by separating the influence of the noise from the intrinsic oscillations over long time scales. We show how this analysis can be used to compute Lyapunov exponents and extended to nonlinear models where the noise has additional resonances.

scholarly journals Solution Of Singularly Perturbed Delay Differential Equations Using Liouville Green Transformation

2021 ◽  
Vol 12 (4) ◽  
pp. 325-335
Author(s):  
M. Adilaxmi , Et. al.
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Perturbation Problem ◽  
Delay Differential ◽  
Singularly Perturbation ◽  
The Given

This paper envisages the use of Liouville Green Transformation to find the solution of singularly perturbed delay differential equations. First, using Taylor series, the given singularly perturbed delay differential equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. The method is demonstrated by implementing several model examples by taking various values for the delay parameter and perturbation parameter.

scholarly journals Oscillation of even-order neutral differential equations via comparison principles

2014 ◽  
Vol 30 (3) ◽  
pp. 293-300
Author(s):  
J. DZURINA ◽  
◽  
B. BACULIKOVA ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Order Differential Equation ◽  
Higher Order ◽  
Comparison Principles ◽  
Neutral Differential Equations ◽  
First Order ◽  
Even Order ◽  
Delay Differential

In the paper we offer oscillation criteria for even-order neutral differential equations, where z(t) = x(t) + p(t)x(τ(t)). Establishing a generalization of Philos and Staikos lemma, we introduce new comparison principles for reducing the examination of the properties of the higher order differential equation onto oscillation of the first order delay differential equations. The results obtained are easily verifiable.

OSCILLATIONS AND ASYMPTOTIC STABILITY OF ENTIRE SOLUTIONS OF LINEAR DELAY DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 10 (4) ◽  
pp. 2069-2076
Author(s):  
Rajeshwari S. ◽  
S.K. Buzurg
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Entire Solutions ◽  
Comparison Result ◽  
Oscillatory Solutions ◽  
Linear Delay ◽  
Delay Differential ◽  
Adequate Condition

Think about the linear delay differential equation, \begin{equation}\label{1} y'(q) + \sum_{n=1}^{m} P_{n}(q) y(q-\tau_{n})=0,\quad q\geq q_{0}, \end{equation} where $P_{n}\in C([q_{0},\infty),R)$ and $\tau_{n}\geq0$ for $n=1,2,\ldots,m$. By investigating the oscillatory solutions of the linear delay differential equations, we offer new adequate condition for the asymptotic stability of the solutions of \eqref{1}. We also produce comparison result and stability of \eqref{1}.

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