A Fourth Order Embedded Runge-Kutta RKACeM(4,4) Method Based on Arithmetic and Centroidal Means with Error Control

In this paper, we introduce a new approach for solving IVPs with error control by formulating an embedded method involving RK methods based on Arithmetic Mean (AM) and Centroidal Mean (CeM). Numerical experiments reveal that the results obtained from this method agree well with the exact solution and also in match with the well known methods like Runge-Kutta Fehlberg (4,5), Runge-Kutta Merson and RK(4,4) introduced by Yaakub and Evans.

Keywords:

• Fourth Order Runge-Kutta Methods
• Arithmetic Mean
• Centroidal Mean
• Rk(4,4)
• Runge-Kutta Fehlberg Method
• Runge-Kutta Merson Method