Boundary value technique based on a fifth derivative method of order 10 for fourth order initial and boundary value problems

作     者：Oladejo, H. B. Jator, S. N. Areo, E. A. 

作者机构：FUTA Dept Math Sci Akure Nigeria Austin Peay State Univ Dept Math & Stat Clarksville TN 37044 USA 

出 版 物：《AFRIKA MATEMATIKA》 (Afr. Mat.)

年 卷 期：2018年第29卷第5-6期

页      面：699-718页

主　　题：Fourth order Initial and Boundary value problems Fifth derivative method Convergence 

摘      要：In this paper, the fourth order ordinary differential equation (ODE) of the form y(()(iv)()) = f (x, y, y , y , y ) subject to initial or boundary conditions is solved directly without reducing the higher ODE into an equivalent first order system. This is accomplished by constructing a continuous fifth derivative method (CFIDM) which is used to produce the main and additional discrete fifth derivative methods (FIDMs). The FIDMs are then assembled and applied as a single block matrix equation to simultaneously provide all approximations on the entire interval of interest for the initial or boundary value problem. The convergence analysis of the method is discussed. The accuracy of the method is illustrated via numerical experiments.