A class of numerical methods for the treatment of delay differential equations is developed. These methods are based on the wellknown Runge-Kutta-Fehlberg methods. The retarded argument is approximated by an appropriate multipoint Hermite Interpolation. The inherent jump discontinuities in the various derivatives of the solution are considered automatically.
Problems with piecewise continuous right-hand side and initial function are treated too. Real-life problems are used for the numerical test and a comparison with other methods published in literature.