Derivation of continuous explicit two-step Runge-Kutta methods of order three

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, AZ 85287, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

We describe a construction of continuous extensions to a new representation of two-step Runge-Kutta methods for ordinary differential equations. This representation makes possible the accurate and reliable estimation of local discretization error, facilitates the efficient implementation of these methods in variable stepsize environment, and adapts readily to the numerical solution of a class of delay differential equations. A number of numerical tests carried out on the obtained methods of order 3 with quadratic interpolants show their efficiency and robust performance which allow them to compete with the state-of-the-art dde23 code from Matlab.