Abstract

ON THE DERIVATION AND IMPLEMENTATION OF A FOUR-STAGE HARMONIC RUNGE-KUTTA SCHEME FOR SOLVING INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS

Ehiemua M. E.,1 Agbeboh G.U.2 and Ataman J.O.3

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A careful search for an appropriate method for solving initial value problems in Ordinary differential equation, has led to the transformation of the arithmetic based Classical Runge-Kutta method, through the process of binomial expansion, to a new scheme that is based on harmonic mean. Consistency and stability of the method were established. This new scheme was implemented upon by solving some selected initial value problems, and comparing with other known methods. The consistency and stability of the method were also established. Keywords: Arithmetic-mean, Harmonic-mean, Binomial expansion, consistency and stability.

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