Abstract:

In this paper, we introduce a new formula of classical fourth-order Runge-Kutta (RK-4) method based on power means (PM). We obtain the new formula called by RK4-PM, by changing arithmetic means on RK-4 method with certain power means i.e. , 𝑝 = 1/2 and furthermore, we also get an area of its stability. Comparing with another RK-4 modification based on geometric means, the numerical results present that RK4-PM has a similar error with other methods.