Nonstandard finite difference schemes for general linear delay differential systems

Abstract

This paper deals with the construction of non‐standard finite difference methods for coupled linear delay differential systems in the general case of non‐commuting matrix coefficients. Based on an expression for the exact solution of the continuous initial value vector delay problem, a family of non‐standard numerical methods of increasing orders is defined. Numerical examples show that the new proposed numerical methods preserve the stability properties of the exact solutions. This work extends previous results for delay systems with commuting matrix coefficients, allowing the use of the new numerical non‐standard methods in more general problems.