Design and Analysis of Some Third Order Explicit Almost Runge-Kutta Methods  

作　　者：Abdulrahman Ndanusa Khadeejah James Audu Abdulrahman Ndanusa;Khadeejah James Audu(Department of Mathematics, Federal University of Technology, Minna, Nigeria)

机构地区：[1]Department of Mathematics, Federal University of Technology, Minna, Nigeria

出　　处：《Applied Mathematics》2016年第1期13-21,共9页应用数学（英文）

摘　　要：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.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.

关 键 词：Almost Runge-Kutta Stability Consistency Convergence Order Conditions Rooted Trees 

分 类 号：O17[理学—数学]