A Block Implicit Advanced Step-point (BIAS) Algorithm for Stiff Differential Systems

In this paper we propose a new block implicit multistep algorithm, which has been constructed with the aim to successfully tackle the numerical solution of stiff ordinary differential equations. In order to maximise the chances of producing a good new scheme, the first mandatory step is to ensure it incorporates very good theoretical properties. A rather detailed account of the new methods is presented and the properties of the algorithm will be discussed in some detail. In the near future we will also have the opportunity to evaluate the implementation potential of the scheme in a future paper.