Simulation of non-linear singular system using RK-Butcher algorithm

Abstract

In this paper, a new method of study on non-linear singular systems from fluid dynamics using the RK-Butcher algorithm is presented. To illustrate the effectiveness of the RK-Butcher algorithm, four cases in non-linear singular systems from fluid dynamics have been considered and compared with the classical fourth order Runge-Kutta, and are found to be very accurate. Local truncation error graphs for the non-linear singular system based nuclear reactor core problem are presented in a graphical form to show the efficiency of this RK-Butcher method. This RK-Butcher algorithm can be easily implemented in a digital computer and the solution can be obtained for any length of time. © 2011 Springer-Verlag.