Attainable order of theP-stable family of certain two-step methods for periodic second order initial value problems

Abstract

Certain two-step hybrid methods are considered for periodic second order initial value problems. Some authors have givenP-stable fourth order formula of this type. We shall give a necessary and sufficient condition for the sixth order formula, for whichP-stability analysis is carried out. Attainable order ofP-stable formula of the type is eventually established as four.