A general formula for the stability functions of a group of implicit advanced step-point (IAS) methods

In this paper we introduce a new general formula that generates the stability functions of a group of methods, which the author has collectively named implicit advanced step-point (IAS) methods. This group of methods encompasses primarily the two implicit advanced step-point (TIAS) methods and the parallel implicit advanced step-point (PIAS) methods, but also the extended and modified extended BDF schemes (EBDF and MEBDF respectively). Furthermore we present, for the first time in a comprehensive way, the TIAS methods. To obtain the distinct stability functions for each of these implicit multistep methods is a quite time-consuming matter and thus an appropriate general formula can substantially facilitate stability analysis and further computational manipulation of these and analogous schemes.