A comparative study of new truncation error estimates and intrinsic accuracies of some higher order Runge-Kutta algorithms

Abstract Runge-Kutta algorithms are tools for the numerical solution of ordinary differential equations. In this paper a comparison is made of the “Classical”, Gill, Merson, England, Nystrom, Fehlberg, and Butcher algorithms, all of fourth order or higher, as to intrinsic accuracy of the native algorithm and accuracy of newly proposed and older truncation error estimates. A new test problem is suggested which can distinguish quantitatively between algorithms. The Butcher is demonstrated to have the highest accuracy and the best truncation error estimate.