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Block Milne’s Implementation For Solving Fourth Order Ordinary Differential Equations

Oghonyon, J. G. and Okunuga, S. A. and Eke, Kanayo Stella and Odetunmibi, , O. A. (2018) Block Milne’s Implementation For Solving Fourth Order Ordinary Differential Equations. Engineering, Technology & Applied Science Research, 8 (3). pp. 2943-2948.

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Abstract

Block predictor-corrector method for solving non-stiff ordinary differential equations (ODEs) started with Milne’s device. Milne’s device is an extension of the block predictor corrector method providing further benefits and better results. This study considers Milne’s devise for solving fourth order ODEs. A combination of Newton’s backward difference interpolation polynomial and numerical integration method are applied and integrated at some selected grid points to formulate the block predictor-corrector method. Moreover, Milne’s devise advances the computational efficiency by applying the chief local truncation error] (CLTE) of the block predictor-corrector method after establishing the order. The numerical results were exhibited to attest the functioning of Milne’s devise in solving fourth order ODEs. The complete results were obtained with the aid of Mathematica 9 kernel for Microsoft Windows. Numerical results showcase that Milne’s device is more effective than existent methods in terms of design new step size, determining the convergence criteria and maximizing errors at all examined convergence levels.

Item Type: Article
Uncontrolled Keywords: Milne’s device; predictor-corrector method; suitable step size; convergence criteria; maximum errors; chief local truncation error]
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Divisions: Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User: Mrs Hannah Akinwumi
Date Deposited: 22 Jun 2018 11:00
Last Modified: 22 Jun 2018 11:00
URI: http://eprints.covenantuniversity.edu.ng/id/eprint/11016

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