In this paper, the technique of discontinuity tracking equations wasproposed in order to deal with the derivative discontinuities in the numerical solution of functionaldifferential equation. This technique will be adapted in a linear multistep method with the support of Runge-Kutta Felhbergstep size strategy. Naturally, the existence of discontinuities will produce a large number of failure steps that can lead to inaccurateresults. In order to get a smooth solution, the technique of detect, locate,and treat ofthe discontinuities hasbeenincluded in the developed algorithm. The numerical results haveshown that this technique not only can improve the solution in terms of smoothness but it also enhancesthe efficiency and accuracy of the proposed method.
