The technique of discontinuity tracking equations for functional differential equations in 1-Point Implicit Method

Abstract

In this paper, the technique of discontinuity tracking equations was proposed in order to deal with the derivative discontinuities in the numerical solution of functional differential equation. This technique will be adapted in a linear multistep method with the support of Runge-Kutta Felhberg step size strategy. Naturally, the existence of discontinuities will produce a large number of failure steps that can lead to inaccurate results. In order to get a smooth solution, the technique of detect, locate, and treat of the discontinuities has been included in the developed algorithm. The numerical results have shown that this technique not only can improve the solution in terms of smoothness but it also enhances the efficiency and accuracy of the proposed method.