Implementation of Nordsieck second derivative methods for stiff ODEs

It is the purpose of this paper to study the construction and implementation of Nordsieck second derivative methods for the numerical integration of stiff systems of first order ordinary differential equations. We construct L  -stable methods of order p=s+1p=s+1, where s   is the number of internal stages, and stage order q=pq=p. The implementation issues including the starting procedures, stage predictors, local error estimation and the changing stepsize are examined. Numerical experiments with methods of orders three and four indicate reliability of the error estimates and efficiency of the methods in a variable stepsize environment.