Comparison of the RK4M4, RK4LIN and RK4M1 methods for systems with time-delays

Abstract

The higher-order Runge-Kutta methods can be used in three different ways when the time- delays occur. The RK4M4, RK4LIN and RK4M1 methods are an application of the most popular fourth-order Runge- Kutta method for time-delays. The RK4M4 method requires a storage of four variables, so it is hardly ever used. Based on the discussion and experimental testing it has been shown that the RK4M4 method nevertheless provides the most significant economy of memory and shortest computing time.