A New Uniform Fourth Order One-Third Step Continuous Block Method for the Direct Solutions of y′′ = f (x, y, y′)

Abstract

In this study, we applied the approach of collocation and interpolation to develop a new fourth order continuous one-third hybrid block method for the solutions of general second order initial value problems of ordinary differential equations. Three discrete schemes were derived from the continuous schemes. The discrete method was analyzed based on the properties of linear multistep methods and the method is found to be zero-stable, consistent and convergent. We reported an improved performance of the new method over the existing methods in the literature by solving four numerical examples and the approximate solutions obtained confirmed the superiority of our new developed scheme when compared with some latest existing approaches.

Derivation of One-Sixth Hybrid Block Method for Solving General First Order Ordinary Differential Equations

“…According to Areo and Rufai (2016), if the order of a linear hybrid multistep method is greater than or equal to one i.e. ( ≥ 1), the method is consistency, since our new proposed methods are of constant order = 4.…”

A variable step-size fourth-derivative hybrid block strategy for integrating third-order IVPs, with applications

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Numerical Solution of Fourth-order Initial Value Problems Using Novel Fourth-order Block Algorithm

“…These setbacks were addressed by Awoyemi [6,7] which was also mentioned in Kayode [12]. While some other scholars solved the fourth-order IVPs directly without reducing to system of first-order IVPs and examples of such authors are Adesanya et al [1], Adeyeye and Omar [2], Akinnukawe and Odekunle [3], Areo and Omole [5], Jator [10], Kayode [11,12], Kuboye et al [13,14], Mohammed [18] to mention few but the accuracy of their schemes in terms of error can be improved upon.…”