This article is made freely available as part of this journal's Open Access: ID | Obayomi-ManuscriptRef.1-ajira140217|
Affiliation.
| Ekiti State University | Department of Mathematics | P. M. B 5363, Ado-Ekiti | Nigeria |
GENERAL INFORMATION
American Journal of Innovative Research & Applied Sciences
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| ISSN: 2429-5396 (e) | www.american-jiras.com|| | Web Site Form: v 0.1.05 | JF 22 Cours, Wellington le Clairval, Lillebonne | France |
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American Journal of innovative Research & Applied Sciences
ISSN 2429-5396 (Online) OCLC Number: 920041286
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| AUGUST | VOLUME 5 | N° 2 | 2017 |
ABSTRACT
Background: This paper presents a new set of non-standard finite difference schemes for the numerical solution of non-linear Clairaut differential equation. Objective: The aim is to use the combination of two modeling techniques based on two non-standard modeling rules to create a qualitatively stable discrete model for the simulation of the solution to the Clairaut equation. We seek to derive finite difference schemes that are stable and correctly replicate the dynamics of the Clairaut equation. Methods: The method employ the use of some normalized denominator functions and non-local transformation of the derivatives base on the required properties stated in the rule 2 of the non-standard modeling rules. Results: We have generated discrete models whose solutions replicate the dynamics of the Clairaut equation Conclusion: The resulting schemes were tested and found to have the same monotonic proprepties as the Clairaut equation.
