2010•Unpublished venueRequires access
Third-order harmonic mean Runge-Kutta formulaefor solving ordinary differential equations
Osama Y. Ababneh, Eddie Shahril Ismail
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Abstract
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