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We present in this paper a new parallel Runge – Kutta method of the second order second stage for solving initial value problems (IVPs) in Ordinary Differential Equations (ODEs) .This new method depending on using the predictor corrector method in the Geometric mean (GM) Runge – Kutta formula, and make it parallel by using the broadening of the computation front.

Parallel Second Order Runge – Kutta new method of the Geometric Mean