A RUNGE-KUTTA METHOD WITH STEPSIZE CONTROL FOR SEPARATED SYSTEMS OF FIRST-ORDER ODES

This paper is concerned with a method, developed earlier, that may be used to solve a system of first-order ODEs separated into two subsystems. Each system may be integrated essentially independently of the other one. A Runge-Kutta technique with automatic stepsize control is developed for the method, taking both truncation and separation errors into account. The paper also provides a proof of the existence of a solution to the separated problem.