A new sixth-order algorithm for general second order ordinary differential equations

A Family of High-Order Multiple Finite Difference Methods for the Direct Solution of the General Second-Order Initial Value Problem

“…While the methods produced good result and saves computer time, the demerit associated with them is that the Taylor's series algorithm involves higher-order partial derivatives that are overlong. Self-starting methods are simply methods that do not require starting values from some other algorithm to be implemented with, and as such, they do not posses the demerits associated with methods proposed in [1,2,3] . Jator and Li [14] proposed a self-starting method of order 5 through the collocation and interpolation method for direct solution to (1).…”

“…Diverse schemes have been presented in literature to solve (1) directly without relaxing it to an equivalent first-order system [1], [2], [3], [4], [7], [9] and [26]. Awoyemi's approach [1,2,3] in solving (1) directly required that the starting values be generated firstly from the Taylor's series algorithm and then applied as Predictor-Corrector methods.…”

“…Awoyemi's approach [1,2,3] in solving (1) directly required that the starting values be generated firstly from the Taylor's series algorithm and then applied as Predictor-Corrector methods. While the methods produced good result and saves computer time, the demerit associated with them is that the Taylor's series algorithm involves higher-order partial derivatives that are overlong.…”

Five Steps Block Predictor-Block Corrector Method for the Solution of <i>y''</i> = <i>f</i> (<i>x</i>,<i>y</i>,<i>y'</i>)

“…Various methods have been proposed by scholars for solving higher order ordinary differential equation (ODE). Notable authors like [1] [7]- [11] have developed direct methods of solving general second order ODE's to cater for the burden inherent in the method of reduction. Now writing computer code is less bur-densome since it no longer requires special ways to incorporate the subroutine to supply the starting values.…”

An Order Six Zero-Stable Method for Direct Solution of Fourth Order Ordinary Differential Equations

“…The approach of reducing such equations to a system of first order equations leads to serious computational burden and wastage in computer time [2], [3] . Many attempts have been made to formulate numerical algorithms capable of solving special problem of type (1) without reducing it to system of first order equations [7], [9], [11], [12] .…”