Trio-Geometric mean-based three-stage Runge–Kutta algorithm to solve initial value problem arising in autonomous systems.

In the present worldwide scenario, plenty of problems arising in science and engineering which can be modeled as differential equations and out of these, autonomous system has become a subject of great interest. Several laws of physics in which time is considered as an independent variable are expressed as autonomous systems. In this paper, Runge–Kutta (RK) three-stage geometric mean method is used to solve the initial value problem arises in autonomous systems. The method is discussed in detail, convergence of method is discussed, the accuracy and efficiency of the method are proved by considering a numerical example. The result is compared to some other methods and proposed method is found to be more efficient. The detailed analysis of error estimation confirms that proposed method is more efficient as compared to other methods. [ABSTRACT FROM AUTHOR]