The Modified Picard method (PSM) for approximating IVPs (in a non-standard numerical fashion) involving ODEs or PDEs has been established as a viable option (see Sochacki and Parker et al.). The form of the approximating method allows itself to be used without much labor on delay differential equations (where the vector field at the current time relies on the state of the system at some earlier time as well as the current time). The properties of the solutions to the DDEs can be different depending on how the delay shows up, hence there are a myriad of subclasses (see Baker, Paul and Wille) and as a consequence, their numerical simulation can be delicate. This jump to DDEs via PSM appears to be possible without worrying about which subclass is involved.
Lehmkuhl, Dustin, "A Numerical Analysis of PSM with Applications to DDEs" (2013). Mathematical Sciences Technical Reports (MSTR). 161.