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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.

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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