A class of hybrid formulae for the numerical integration of stiff systems

Abstract

A class of hybrid formulae suitable for the numerical integration of stiff systems of first order ordinary differential equations is presented. These formulae are defined in a predictor-corrector mode and contain an off-step pointxn+v, which is distinct from the points defined by the step used. The parameterv is examined in an attempt to obtain better stability properties and higher order formulae of one step only. We obtain order five and eitherA-stability or stiff-stability according to the values ofv used. Some numerical results are presented.