On generalized impulsive piecewise constant delay differential equations

2015 ◽  
Vol 58 (9) ◽  
pp. 1981-2002 ◽  
Author(s):  
Kuo-Shou Chiu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Constant Delay ◽  
Piecewise Constant ◽  
Delay Differential

scholarly journals Numerical Solution of Piecewise Constant Delay Systems Based on a Hybrid Framework

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
H. R. Marzban ◽  
S. Hajiabdolrahmani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Operational Matrix ◽  
Delay Systems ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Constant Delay ◽  
Piecewise Constant ◽  
Delay Function ◽  
Delay Differential

An efficient numerical scheme for solving delay differential equations with a piecewise constant delay function is developed in this paper. The proposed approach is based on a hybrid of block-pulse functions and Taylor’s polynomials. The operational matrix of delay corresponding to the proposed hybrid functions is introduced. The sparsity of this matrix significantly reduces the computation time and memory requirement. The operational matrices of integration, delay, and product are employed to transform the problem under consideration into a system of algebraic equations. It is shown that the developed approach is also applicable to a special class of nonlinear piecewise constant delay differential equations. Several numerical experiments are examined to verify the validity and applicability of the presented technique.

NUMERICAL BIFURCATION ANALYSIS OF DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

2001 ◽  
Vol 11 (03) ◽  
pp. 737-753 ◽  
Author(s):  
TATYANA LUZYANINA ◽  
KOEN ENGELBORGHS ◽  
DIRK ROOSE
Keyword(s):  
Differential Equations ◽  
Bifurcation Analysis ◽  
Delay Differential Equations ◽  
Constant Delay ◽  
State Dependent ◽  
State Dependent Delay ◽  
Numerical Bifurcation ◽  
Delay Differential ◽  
Steady State Solutions ◽  
Numerical Bifurcation Analysis

In this paper we apply existing numerical methods for bifurcation analysis of delay differential equations with constant delay to equations with state-dependent delay. In particular, we study the computation, continuation and stability analysis of steady state solutions and periodic solutions. We collect the relevant theory and describe open theoretical problems in the context of bifurcation analysis. We present computational results for two examples and compare with analytical results whenever possible.

scholarly journals On a class of third order neutral delay differential equations with piecewise constant argument

1994 ◽  
Vol 17 (1) ◽  
pp. 113-117 ◽  
Author(s):  
Garyfalos Papaschinopoulos
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Third Order ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
Constant Argument

In this paper we study existence, uniqueness and asymptotic stability of the solutions of a class of third order neutral delay differential equations with piecewise constant argument.

scholarly journals Word series high-order averaging of highly oscillatory differential equations with delay

2019 ◽  
Vol 4 (2) ◽  
pp. 445-454 ◽  
Author(s):  
J. M. Sanz-Serna ◽  
Beibei Zhu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
High Order ◽  
Constant Delay ◽  
Integer Multiple ◽  
Averaged Equations ◽  
Highly Oscillatory ◽  
Highly Oscillatory Differential Equations ◽  
Delay Differential ◽  
Equations With Delay

AbstractWe show that, when the delay is an integer multiple of the forcing period, it is possible to obtain easily high-order averaged versions of periodically forced systems of delay differential equations with constant delay. Our approach is based on the use of word series techniques to obtain high-order averaged equations for differential equations without delay.

Sign in / Sign up

Export Citation Format

Share Document