Absolute stability properties of the explicit linear 3-step formulae

Abstract

A three-parameter family of explicit linear 3-step formulae is derived. The conditions which ensure zero-stability of the formulae in the family are formulated. The absolute stability properties of the zero-stable formulae in the family are investigated both for p = 3 and p = 2 where p is the order of the formulae under consideration. Some numerical experiments are carried out in order to illustrate that formulae with good absolute stability properties can efficiently be used in the numerical solution of problems in which the absolute stability properties are dominant.