scholarly journals Nonstandard finite difference schemes for general linear delay differential systems

2020 ◽  
Author(s):  
M. Ángeles Castro ◽  
Antonio Sirvent ◽  
Francisco Rodríguez
Keyword(s):  
Finite Difference ◽  
Difference Schemes ◽  
General Linear ◽  
Finite Difference Schemes ◽  
Differential Systems ◽  
Linear Delay ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Nonstandard Finite Difference

scholarly journals Exact and Nonstandard Finite Difference Schemes for Coupled Linear Delay Differential Systems

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1038 ◽  
Author(s):  
María Ángeles Castro ◽  
Miguel Antonio García ◽  
José Antonio Martín ◽  
Francisco Rodríguez
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Linear Delay ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Consistency Properties ◽  
Nonstandard Finite Difference

In recent works, exact and nonstandard finite difference schemes for scalar first order linear delay differential equations have been proposed. The aim of the present work is to extend these previous results to systems of coupled delay differential equations X ′ ( t ) = A X ( t ) + B X ( t - τ ) , where X is a vector, and A and B are commuting real matrices, in general not simultaneously diagonalizable. Based on a constructive expression for the exact solution of the vector equation, an exact scheme is obtained, and different nonstandard numerical schemes of increasing order are proposed. Dynamic consistency properties of the new nonstandard schemes are illustrated with numerical examples, and proved for a class of methods.

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