A third order Runge-Kutta method based on a linear combination of arithmetic mean, geometric mean and centroidal mean for first order differential equation

Differential Equations are indispensable for modelling the real world phenomena. Numerical methods are helpful to arrive at a solution of the problems where it is difficult to find the exact solution. A new third order Runge-Kutta method based on a linear combination of arithmetic mean, geometric mean and centroidal mean is derived to solve initial value problems. Some numerical examples are given to show the effectiveness of the proposed method.