In this paper, we derive a general singulo oscillatory – stiff rational integrator of order (S+3) for s = 0, 1, 2, 3, 4,… for the solution of initial value problems in ordinary differential systems that are singular, oscillatory or stiff. We compared our integrators with certain maximum order second derivative hybrid multi-step methods, certain Tau and Euler methods, the adaptive implicit and classical Runge-Kutta methods and some existing conventional methods. Our results show good improvement over the existing methods compared with.
Key words: Rational integrator, initial value problems, stability, convergence, consistency.
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