Third-order harmonic mean Runge-Kutta formulae for solving ordinary differential equations - Rokiah @ Rozita Ahmad; Osama Yusuf Ababneh; Eddie Shahril Ismail (Penerbit Universiti Kebangsaan Malaysia, 2010)

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The conventional arithmetic mean used in the formulation of the new Runge–Kutta method has resulted in the introduction of a number of new formulae for the numerical solution of ordinary differential equations. This study discusses the derivation of a third-order Runge- Kutta method using the harmonic mean averaging of the functional values. The accuracy of these new Runge-Kutta formulae is numerically tested and the stability is examined