Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 21 Issue 4

© 2021. Skwame, Yusuf, Raymond, Dominic, Tumba, Pius & Adiku, Lydia. This research/review article is distributed under the terms of the Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). You must give appropriate credit to authors and reference this article if parts of the article are reproduced in any manner. Applicable licensing terms are at https://creativecommons.org/ licenses/by-nc-nd/4.0/. Half-Step Implicit Linear Multistep Hybrid Block Third Derivative Methods of order Four for the Solution of Third order Ordinary Differential Equations By Skwame, Yusuf, Raymond, Dominic, Tumba, Pius & Adiku, Lydia Adamawa State University Abstract- This paper proposes a half-step third derivative hybrid block method with two cases of order four for solution of third Order Ordinary Differential Equations. Method of interpolation and collocation of power series approximate solution was used to generate the continuous hybrid linear multistep method, which was then evaluated at non-interpolating points to give a continuous block method. The discrete block method was recovered when the continuous block was evaluated at all step points. The basic properties of the methods were investigated and were found to be zero-stable, consistent and convergent. The develop half-step method is applied to solve some third order initial value problems of ordinary differential equations and from the numerical results obtained, it is observed that our methods gives better approximation than the existing method compared with. Keywords: half-step, hybrid block method, third derivative. GJSFR-F Classification: MSC 2010: 33E30 HalfStepImplicitLinearMultistepHybridBlockThirdDerivativeMethodsoforderFourfortheSolutionofThirdorderOrdinaryDifferentialEquations Strictly as per the compliance and regulations of: Global Journal of Science Frontier Research: F Mathematics and Decision Sciences Volume 21 Issue 4 Version 1.0 Year 2021 Type: Double Blind Peer Reviewed International Research Journal Publisher: Global Journals Online ISSN: 2249-4626 & Print ISSN: 0975-5896