This work presents an analysis of approximation schemes for initial value problems of differential–difference equations based on sequences of Cauchy problems for systems of ordinary differential equations of classical and higher-order accuracy. Convergence conditions and accuracy properties of the approximation schemes are established. An npm package and a web application implemented in TypeScript have been developed to automate the numerical simulation of delay systems using the algorithms proposed in the study. Numerical experiments for representative benchmark examples are carried out to demonstrate the performance and validity of the schemes.

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