Nordsieck representation of two-step Runge--Kutta methods for ordinary differential equations

Authors:
Z. Bartoszewski;Z. Jackiewicz
Affiliations:
Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-952 Gdańsk, Poland;Department of Mathematics, Arizona State University, Tempe, Arizona 85287, USA
Venue:
Applied Numerical Mathematics
Year:
2005

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Abstract

We describe a new representation of explicit two-step Runge-Kutta methods for ordinary differential equations. This representation makes it possible for the accurate and reliable estimation of local discretization error and facilitates the efficient implementation of these methods in a variable stepsize environment.