Coefficients for studying one-step rational schemes for IVPs in ODEs: II

In [1], we derived variable order, variable stepsize, one-step nonlinear methods in which global formulation is facilitated by defining some certain coefficients. The analysis has a broader application and facilitates the derivation of new formulae. The methods are based on a variant self-adjusting rational interpolant of Luke et al. [2] and Otunta and Ikhile [3,4]. In this paper, we motivate an extension of this analysis to obtain a more generalized class of the rational methods in [1] for an arbitrarily desired order.