Abstract
This paper presents a class of hybrid one-step methods that are obtained by using Cramer's rule and rational approximation 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.
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