International journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN:2313-626X

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 Volume 5, Issue 8 (August 2018), Pages: 18-23

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 Original Research Paper

 Title: Programming codes of block-Milne's device for solving fourth-order ODEs

 Author(s): Oghonyon Jimevwo Godwin *, Bishop Sheila Amina, Eke Stella Kanayo

 Affiliation(s):

 Department of Mathematics, College of Science, Covenant University, P.M.B. 1023, Ota, Ogun State, Nigeria

 https://doi.org/10.21833/ijaas.2018.08.003

 Full Text - PDF          XML

 Abstract:

Block-Milne’s device is an extension of block-predictor-corrector method and specifically developed to design a worthy step size, resolve the convergence criteria and maximize error. In this study, programming codes of block- Milne’s device (P-CB-MD) for solving fourth order ODEs are considered. Collocation and interpolation with power series as the basic solution are used to devise P-CB-MD. Analysing the P-CB-MD will give rise to the principal local truncation error (PLTE) after determining the order. The P-CB-MD for solving fourth order ODEs is written using Mathematica which can be utilized to evaluate and produce the mathematical results. The P-CB-MD is very useful to demonstrate speed, efficiency and accuracy compare to manual computation applied. Some selected problems were solved and compared with existing methods. This was made realizable with the support of the named computational benefits. 

 © 2018 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Block-Milne’s device, Mathematica programming codes, Convergence limit, Max calculated errors, Principal local truncation error

 Article History: Received 11 January 2018, Received in revised form 18 May 2018, Accepted 20 May 2018

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2018.08.003

 Citation:

 Oghonyon JG, Bishop SA, and Eke SK (2018). Programming codes of block-Milne's device for solving fourth-order ODEs. International Journal of Advanced and Applied Sciences, 5(8): 18-23

 Permanent Link:

 http://www.science-gate.com/IJAAS/2018/V5I8/Godwin.html

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