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

作     者：Abdulrahman Ndanusa Khadeejah James Audu Abdulrahman Ndanusa;Khadeejah James Audu

作者机构：Department of Mathematics Federal University of Technology Minna Nigeria 

出 版 物：《Applied Mathematics》 (应用数学（英文）)

年 卷 期：2016年第7卷第1期

页      码：13-21页

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.

主 题 词：Almost Runge-Kutta Stability Consistency Convergence Order Conditions Rooted Trees 

学科分类：07[理学] 0701[理学-数学类] 070101[070101] 

D　O　I：10.4236/am.2016.71002

馆 藏 号：203219999...