Functional-Differential and Functional Equations with Rescaling

1995 ◽  
pp. 100-111 ◽  
Author(s):  
Gregory Derfel
Keyword(s):  
Functional Equations ◽  
Functional Differential

Variation of constants for hybrid systems of functional differential equations

1995 ◽  
Vol 125 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Jack K. Hale ◽  
Wenzhang Huang
Keyword(s):  
Differential Equations ◽  
Hybrid Systems ◽  
Difference Equations ◽  
Delay Differential Equations ◽  
Functional Equations ◽  
Functional Differential Equations ◽  
Variation Of Constants Formula ◽  
Variation Of Constants ◽  
Functional Differential ◽  
Delay Differential

The objective is to derive a variation of constants formula for systems of functional differential equations (or delay differential equations) coupled with functional equations (or difference equations). The difficulties arise because of the constraints imposed by the functional equations.

scholarly journals Stability Analysis of Runge-Kutta Methods for Nonlinear Functional Differential and Functional Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yuexin Yu ◽  
Zhongyan Liu ◽  
Liping Wen
Keyword(s):  
Stability Analysis ◽  
Numerical Stability ◽  
Functional Equations ◽  
Numerical Test ◽  
Sufficient Conditions ◽  
Nonlinear Functional ◽  
Runge Kutta ◽  
Functional Differential ◽  
The Stability ◽  
Theoretical Results

This paper is concerned with the numerical stability of Runge-Kutta methods for a class of nonlinear functional differential and functional equations. The sufficient conditions for the stability and asymptotic stability of(k,l)-algebraically stable Runge-Kutta methods are derived. A numerical test is given to confirm the theoretical results.

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