Author(s)

Abdulrahman Ndanusa, Khadeejah James Audu

Department of Mathematics, Federal University of Technology, Minna, Nigeria.

In this paper, we propose two new explicit Almost Runge-Kutta (ARK) methods, ARK3 (a three stage third order method, i.e., s = p = 3) and ARK34 (a four-stage third-order method, i.e., s = 4, p = 3), for the numerical solution of initial value problems (IVPs). The methods are derived through the application of order and stability conditions normally associated with Runge-Kutta methods; the derived methods are further tested for consistency and stability, a necessary requirement for convergence of any numerical scheme; they are shown to satisfy the criteria for both consistency and stability; hence their convergence is guaranteed. Numerical experiments carried out further justified the efficiency of the methods.

Almost Runge-Kutta, Stability, Consistency, Convergence, Order Conditions, Rooted Trees

Ndanusa, A. and Audu, K. (2016) Design and Analysis of Some Third Order Explicit Almost Runge-Kutta Methods. Applied Mathematics, 7, 13-21. doi: 10.4236/am.2016.71002.