A New Hybrid Block Method for the Solution of General Third Order Initial Value Problems of Ordinary Differential Equations

Abstract

In this paper, we develop an order six block method using method of collocation and interpolation of power series approximate solution to give a system of non linear equations which is solved to give a continuous hybrid linear multistep method . The continous hybrid linear multistep method is solved for the independent solutions to give a continous hybrid block method which is then evaluated at some selected grid points to give a discrete block method . The basic properties of the discrete block method was investigated and found to be zero stable, consistent and convergent. The derived scheme was tested on some numerical examples and was found to give better approximation than the existing method.

An Eight Order Two-Step Taylor Series Algorithm for the Numerical Solutions of Initial Value Problems of Second Order Ordinary Differential Equations

“…Also, some notable scholars improve on the predictor-corrector method for solving ordinary differential equations of higher orders, for instance, Jator and Li [18] proposed five-step and four-step methods respectively in which they adopted a continuous LMM to obtain finite difference method. Moreover, Adesanya [19] adopted a method of collocation and interpolation to develop a continuous LMM which is evaluated at different grid points to give discret methods that generate independent solutions. Others that adopted block methods include Badmus and Yahaya [20].…”

Application of single step with three generalized hybrid points block method for solving third order ordinary differential equations

“…Reduction approach has been identified to have some drawbacks which include computer burden and alots of human efforts [1,7,10] and [14]. Because of this, many researchers have attempted to solve Equation (1) directly .…”

“…Because of this, many researchers have attempted to solve Equation (1) directly . Worthy of note are those of [4,5,6,12] and [13].…”

Derivation of a Six-Step Block Method for Direct Solution of Second Order Ordinary Differential Equations

“…Direct solution of higher order ODEs has been found to be more accurate than when they are reduced to their equivalent system of first order ODEs (see [4], [8], [3], [9]). A lot of scholars such as Awoyemi [4][5] and Omar & Suleiman [11][12][13] amongst others have worked on the derivation of direct method for solving higher order ordinary differential equations.…”

“…al. [2] proposed two steps block method for the direct solution of (1). An improved parallel method with a step-length of three was developed by Yayaha [10] for solving (1) directly.…”