A nonlinear variation-of-constants formula for functional differential equations

1972 ◽  
Vol 6 (3) ◽  
pp. 343-352 ◽  
Author(s):  
Gerald A. Shanholt
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Nonlinear Variation ◽  
Variation Of Constants Formula ◽  
Variation Of Constants ◽  
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.

Stability of Implicit Difference Equations Generated by Parabolic Functional Differential Problems

2007 ◽  
Vol 7 (1) ◽  
pp. 68-82
Author(s):  
K. Kropielnicka
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Initial Boundary ◽  
Numerical Examples ◽  
Convergence Results ◽  
Nonlinear Parabolic ◽  
Implicit Difference Methods ◽  
Neumann Type ◽  
Difference Methods ◽  
Functional Differential

AbstractA general class of implicit difference methods for nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type is constructed. Convergence results are proved by means of consistency and stability arguments. It is assumed that given functions satisfy nonlinear estimates of Perron type with respect to functional variables. Differential equations with deviated variables and differential integral problems can be obtained from a general model by specializing given operators. The results are illustrated by numerical examples.

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