Preprint series: 07-01 , Reports on Numerical Mathematics
Abstract: We describe a construction of implicit two--step Runge--Kutta methods
for ordinary differential equations in Nordsieck form and their
continuous extensions. This representation allows accurate and reliable
estimation of the local discretization errors and the application to
differential equations with delays.
Two stiffly accurate methods of order three with quadratic interpolants
are derived, one of it is shown to be L-stable.
Keywords: Two--step Runge--Kutta methods, stiffly accurate methods, continuous interpolants, delay differential equations, Nordsieck representation
Upload: 2007-01-10