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There exist excellent codes for an efficient numerical treatment of stiff anddifferential-algebraic problems. Let us mention {\sc Radau5} which is based onthe $3$-stage Radau IIA collocation method, and its extension to problems withdiscrete delays {\sc Radar5}. The aim of the present work is to present atechnique that permits a direct application of these codes to problems having aright-hand side with an additional distributed delay term (which is a specialcase of an integro-differential equation). Models with distributed delays areof increasing importance in pharmacodynamics and pharmacokinetics for the studyof the interaction between drugs and the body.  The main idea is to approximate the distribution kernel of the integral termby a sum of exponential functions or by a quasi-polynomial expansion, and thento transform the distributed (integral) delay term into a set of ordinarydifferential equations. This set is typically stiff and, for some distributionkernels (e.g., Pareto distribution), it contains discrete delay terms withconstant delay. The original equations augmented by this set of ordinarydifferential equations can have a very large dimension, and a careful treatmentof the solution of the arising linear systems is necessary.  The use of the codes {\sc Radau5} and {\sc Radar5} is illustrated at threeexamples (two test equations and one problem taken from pharmacodynamics). Thedriver programs for these examples are publicly available from the homepages ofthe authors.

Applying stiff integrators for ODEs and DDEs to problems with distributed delays