Solving delay differential equations in S-ADAPT by method of steps

2013 ◽  
Vol 111 (3) ◽  
pp. 715-734 ◽  
Author(s):  
Robert J. Bauer ◽  
Gary Mo ◽  
Wojciech Krzyzanski
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Method Of Steps ◽  
Delay Differential

scholarly journals Constructive solution of coupled second order delay differential equations with variable coefficients

1995 ◽  
Vol 18 (4) ◽  
pp. 689-700
Author(s):  
R. J. Villanueva ◽  
A. Hervas ◽  
M. V. Ferrer
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Bounded Domain ◽  
Delay Differential Equations ◽  
Approximation Error ◽  
Variable Coefficients ◽  
Second Order ◽  
Initial Value ◽  
Method Of Steps ◽  
Delay Differential

In this paper, we study initial value problems for coupld second order delay differential equations with variable coefficients. By means of the application of the method of steps and the method of Frobenius, the exact solution of the problem is constrcted. Then, in a bounded domain, a finite analytic solution with error bounds is provided. Given an admissible errorϵwe give the number of terms to be taken in the infinite series exact solution so that the approximation error be smaller than in the bounded domain.

scholarly journals Dependence of Dynamics of a System of Two Coupled Generators with Delayed Feedback on the Sign of Coupling

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1790
Author(s):  
Alexandra Kashchenko
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Coupling Parameter ◽  
Delayed Feedback ◽  
Structure Of Solutions ◽  
Asymptotics Of Solutions ◽  
Finite Dimensional ◽  
Method Of Steps ◽  
Delay Differential ◽  
Negative Coupling

In this paper, we study the nonlocal dynamics of a system of delay differential equations with large parameters. This system simulates coupled generators with delayed feedback. Using the method of steps, we construct asymptotics of solutions. By these asymptotics, we construct a special finite-dimensional map. This map helps us to determine the structure of solutions. We study the dependence of solutions on the coupling parameter and show that the dynamics of the system is significantly different in the case of positive coupling and in the case of negative coupling.

A New Look at the Stability Analysis of Delay-Differential Equations

2005 ◽  
Author(s):  
Tama´s Kalma´r-Nagy
Keyword(s):  
Difference Equation ◽  
Differential Equations ◽  
Characteristic Equation ◽  
Delay Differential Equations ◽  
Linear Delay ◽  
The Laplace Transform ◽  
Method Of Steps ◽  
The Difference ◽  
The Stability ◽  
Delay Differential

It is shown that the method of steps for linear delay-differential equations combined with the Laplace-transform can be used to determine the stability of the equation. The result of the method is an infinite dimensional difference equation whose stability corresponds to that of the transcendental characteristic equation. Truncations of this difference equation are used to construct numerical stability charts. The method is demonstrated on a first and second order delay equation. Correspondence between the transcendental characteristic equation and the difference equation is proved for the first order case.

scholarly journals Hermite Wavelet Method for Fractional Delay Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Umer Saeed ◽  
Mujeeb ur Rehman
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Wavelet Method ◽  
Numerical Examples ◽  
Method Of Steps ◽  
Fractional Delay ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

We proposed a method by utilizing method of steps and Hermite wavelet method, for solving the fractional delay differential equations. This technique first converts the fractional delay differential equation to a fractional nondelay differential equation and then applies the Hermite wavelet method on the obtained fractional nondelay differential equation to find the solution. Several numerical examples are solved to show the applicability of the proposed method.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

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