An Explicit and Semi - Implicit Rational Runge - Kutta Schemes for Approximation of Second Order Ordinary Differential Equations

In this paper, two schemes of one stage are derived, an Explicit Rational Runge – Kutta and a Semi – Implicit Rational Runge – Kutta method were derived using Taylor and Binomial series expansion for the solution of general second order initial value problems of ordinary differential equations with constant step size. The analysis of the develop methods was carried out and found to be consistent and convergent and A – stable. The accuracy of the methods were tested on some examples and found to give better approximations. Keywords: Explicit, Semi – Implicit Ration Runge – Kutta, Taylor series, Binomial Expansion, A – Stable.