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We introduce a new method for solving Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs), by making a mixing between the Forward (Predictor) – Backward (Corrector) technique and used it in the Contra Harmonic mean formula, this new method give us a parallelism in numerical calculations and it is more accurate than the old classical Runge – Kutta formula of the same order.

A new method using the Forward Backward technique with Contra Harmonic mean formula