Numerical Strategies for the System of Second Order IVPs Using the RK-Butcher Algorithms

In this paper, a new method of analysis for second order initial value problems using the RKButcher algorithms is presented. To illustrate the effectiveness of the RK-Butcher algorithms, seven problems of different kinds have been considered and the solutions were obtained using the RK method based on Arithmetic mean (RKAM), Centroidal mean (RKCeM) and the RK-Butcher Algorithms and are compared with the exact solutions of the seven problems. Stability regions for the RK-Butcher algorithm, RKAM and RKCeM methods are presented. Error graphs for the second order initial value problems have been presented in a graphical form to show the efficiency of this RK-Butcher algorithm. This RK-Butcher algorithm can be easily implemented in a digital computer and the solution can be obtained for any length of time.