On the connection between the Runge-Kutta method and Picard's method

Abstract The Runge-Kutta method for the numerical solution of Cauchy's problem for a system of ordinary differential equations has an obvious iterative character. As demonstrated In this paper, this phenomenon arises from the connection between the Runge-Kutta method and Picard's iterative method. The estimation of error for the Runge-Kutta method is based on this connection.