A Class of Multiderivative Hybrid One-step Methods

This paper presents a class of hybrid one-step methods that are obtained by using Cramer’s rule and rational approximations to function exp(q). The algorithms fall into the catalogue of implicit formula, which involves sth order derivative and s+1 free parameters. The order of the algorithms satisfies s+1≤p≤2s+2. The stability of the methods is also studied, necessary and sufficient conditions for A-stability and L-stability are given. In addition, some examples are also given to demonstrate the method presented.