Implementation of two-step Runge-Kutta methods for ordinary differential equations

We investigate the potential for efficient implementation of two-step Runge-Kutta methods (TSRK), a new class of methods introduced recently by Jackiewicz and Tracogna for numerical integration of ordinary differential equations. The implementation issues addressed are the local error estimation, changing stepsize using Nordsieck technique and construction of interpolants. The numerical experiments indicate that the constructed error estimates are very reliable in a fixed and variable stepsize environment.