(1) Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA;(2) Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA
Abstract:
Local and global error for Two-Step Runge-Kutta (TSRK) methods are analyzed using the theory of B-series. Global error bounds are derived in both constant and variable stepsize environments. An embedded TSRK pair is constructed and compared with the RK5(4)6M pair of Dormand and Prince on the DETEST set of problems. Numerical results show that the TSRK performs competitively with the RK method.