Non-linear singular systems using RK–Butcher algorithms

Abstract

The Runge–Kutta (RK)–Butcher algorithm is used to study time-invariant and time-varying non-linear singular systems. The results (discrete solutions) obtained using the RK method based on the arithmetic mean (RKAM), single-term Walsh series (STWS) and RK–Butcher algorithms are compared with the exact solutions of the non-linear singular systems for the time-invariant and time-varying cases. It is found that the solution obtained using the RK–Butcher algorithm is closer to the exact solutions of the non-linear singular systems. Stability regions for the RKAM, STWS and RK–Butcher algorithms are presented. Error graphs for discrete and exact solutions are presented in a graphical form to highlight the efficiency of this method. The RK–Butcher algorithm can easily be implemented using a digital computer and the solution can be obtained for any length of time for both time-invariant and time-varying cases for these non-linear singular systems, which is an added advantage of this algorithm.