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

摘要

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 oflocal 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 dde2 3 code from Matlab. (c) 2006 Elsevier B.V. All rights reserved.