IMPROVED THIRD ORDER RUNGE-KUTTA METHODS BASED ON THE CONVEX COMBINATION OF VARIETY OF MEAN

This paper presents the construction of a 3-stage explicit Runge Kutta method of order three based on the convex combination of Arithmetic mean, Harmonic mean and Heronian mean which was recently constructed base on the linear combination of Arithmetic mean, Geometric mean and Harmonic mean as against the constructions based on Arithmetic mean, Heronian mean, Contra-Harmonic mean, Harmonic mean and Geometric mean. The region of absolute stability of the new method was established. Numerical experiments were performed on some initial value problems and the results showed that the new method compete well enough when compared with some existing 3-stage explicit Runge Kutta methods.