… We note that the rational methods presented in this paper are component applicable to IVP
systems in the sense of Lambert [22], unlike the second derivative methods (SDM) of Enright […

… considered a variant one step rational nonlinear method of Otunta and Ikhile [2] in an approach
of globally formulating rational methods of arbitrary order. In the forthcoming Part II of this …

… Methods of [2] constitute special forms of (1.19). We provide a … of rational schemes by defining
some certain coefficients C} i), j … II, for further recursive form of computing these coefficients. …

… , he too is interested primarily in one-step formulas. On the other hand… Introduce the new
coefficients Cs+l 1, as+l,j … behaviour if its stepsize selection scheme is not suitably constrained. …

… The stability of the new scheme is also analyzed. We compared … phase lag, we study the
following general four-step method: … The Taylor series expansion of the coefficient A 2 v is given …

… compare Van Nierkerk's [2] rational one-step method with the … This scheme is a class of k-step
formula of order k. In practice … constants previously obtained stays exactly the same, hence …

… The convetional one-step scheme is given by: … For Example 2, we consider a singular example
which has singular … (2002), Coefficients for studying one-step rational schemes for IVPs in …

… We propose a nonlinear one-step second derivative method (… based on a rational function
is proposed since rational are … In order to determine the coefficients ( a 0 , a 1 , a 2 , a 3 ) in (2), …

… rational type, which is observed to be useful to deal with IVPs, … fifth order rational method,
we put the value of j = 4 in (2) to … We assume a system of s ordinary differential equations in the …

… = 2 y n 2 + 2 h y n f n − 2 h α y n 2 A n 2 y n − 2 h α A n y n − h … high-order explicit one-step
schemes that exhibit exceptional … work to study the construction of explicit high-order one-step …