Über den Fehler des Runge-Kutta-Verfahrens für die numerische Integration gewöhnlicher Differentialgleichungenn-ter Ordnung

Summary

For the numerical solution of an ordinary differential equation of then-th order (1) with the initial conditions (2)Zurmühl has developed general Runge-Kutta formulas which integrate this equation directly without separating it into a system ofn equations of the first order. In the present paper some estimations of the errors of this Runge-Kutta method are given, which are valid for any value ofn. It is assumed that the functionf(x, y, y′,...) on the right side of the differential equation and its partial derivatives up to the fourth order are one-valued and continuous in a certain neighbourhood of the initial values and that bounds of these functions are known.