On fitting stability regions of second derivative multi-step methods

Abstract

A class of second-derivative two-step methods, S(2), with order 5 and depending on two parameters - which are used to adapt the stability region while minimizing the truncation error coefficient - is constructed. An analysis of two subclasses of S(2)-A(0) stable methods and methods with finite stability interval - with their stability and accuracy properties is presented. Numerical examples are also included.