Retarded differential equations (RDEs) are differential equations having retarded arguments. They arise in many realistic models of problems in science, engineering, and medicine, where there is a time lag or after-effect. Numerical techniques for such problems may be regarded as extensions of dense-output methods for ordinary differential equations (ODEs), but scalar RDEs are inherently infinite dimensional with a richer structure than their ODE counterparts. We give background material, develop a theoretical foundation for the basic numerics, and give some results not previously published.
Baker, C. T. H. (2000). Retarded differential equations. Journal of Computational and Applied Mathematics, 125(1–2), 309–335. https://doi.org/10.1016/S0377-0427(00)00476-3