Variation of parameters formula and Gronwall inequality for differential equations with a general piecewise constant argument

2011 ◽  
Vol 27 (4) ◽  
pp. 561-568 ◽  
Author(s):  
Kuo-Shou Chiu ◽  
Manuel Pinto
Keyword(s):  
Differential Equations ◽  
Gronwall Inequality ◽  
Piecewise Constant ◽  
Variation Of Parameters ◽  
Piecewise Constant Argument ◽  
Grönwall Inequality ◽  
Variation Of Parameters Formula ◽  
Constant Argument

Application of gPCRK Methods to Nonlinear Random Differential Equations with Piecewise Constant Argument

2017 ◽  
Vol 7 (2) ◽  
pp. 306-324
Author(s):  
Chengjian Zhang ◽  
Wenjie Shi
Keyword(s):  
Differential Equations ◽  
Polynomial Chaos ◽  
Piecewise Constant ◽  
Aliasing Error ◽  
Piecewise Constant Argument ◽  
Finite Dimensional ◽  
Discretisation Error ◽  
Random Differential Equations ◽  
Projection Error ◽  
Constant Argument

AbstractWe propose a class of numerical methods for solving nonlinear random differential equations with piecewise constant argument, called gPCRK methods as they combine generalised polynomial chaos with Runge-Kutta methods. An error analysis is presented involving the error arising from a finite-dimensional noise assumption, the projection error, the aliasing error and the discretisation error. A numerical example is given to illustrate the effectiveness of this approach.

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.

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