Computational fixed-point theory for differential delay equations with multiple time lags
نویسندگان
چکیده
منابع مشابه
Delay-Differential Equations with Constant Lags
This article concerns delay–differential equations (DDEs) with constant lags. DDEs increasingly are being used to model various phenomena in mathematics and the physical sciences. For such equations the value of the derivative at any time depends on the solution at a previous “lagged” time. Although solving DDEs is similar in some respects to solving ordinary differential equations (ODEs), it d...
متن کاملComputational Method for Fractional-Order Stochastic Delay Differential Equations
Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...
متن کاملBoundary layer phenomena for differential-delay equations with state-dependent time lags: III
We consider a class of singularly perturbed delay-differential equations of the form e ’ xðtÞ 1⁄4 f ðxðtÞ; xðt rÞÞ; where r 1⁄4 rðxðtÞÞ is a state-dependent delay. We study the asymptotic shape, as e-0; of slowly oscillating periodic solutions. In particular, we show that the limiting shape of such solutions can be explicitly described by the solution of a pair of so-called max-plus equations. ...
متن کاملBoundary Layer Phenomena for Differential-Delay Equations with State-Dependent Time Lags, L
In this paper we begin a study of the differential-delay equation ex ' ( t ) = x ( t ) + f ( x ( t r ) ) , r = r ( x ( t ) ) . We prove the existence of periodic solutions for 0 < e < e0, where e0 is an optimal positive number. We investigate regularity and monotonicity properties of solutions x ( t ) which are defined for all t and of associated functions like tl (t) = t r ( x ( t ) ) . We beg...
متن کاملExpansion methods for solving integral equations with multiple time lags using Bernstein polynomial of the second kind
In this paper, the Bernstein polynomials are used to approximate the solutions of linear integral equations with multiple time lags (IEMTL) through expansion methods (collocation method, partition method, Galerkin method). The method is discussed in detail and illustrated by solving some numerical examples. Comparison between the exact and approximated results obtained from these methods is car...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2012
ISSN: 0022-0396
DOI: 10.1016/j.jde.2011.11.020