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

In [1,2], we considered an approach of global formulation of one-step integrators of arbitrary order on a self-adjusting rational approximant by introducing the constants C(s)j, s = 1, 2, 3, …, j = 2, 3, …, j − s ≥ 1. In the present consideration, we motivate a study of this approach to derive a class of one-step methods of variable order and variable stepsize.