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2019 | 118 | 236-250
Article title

A Two-step Hybrid Block Method for the Numerical Integration of Higher Order Initial Value Problems of Ordinary Differential Equations

Content
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EN
Abstracts
EN
In this paper, a two-step implicit hybrid block multistep method is proposed for the approximate solution of higher order ordinary differential equations with a specification of fourth order. The study provides the use of both collocation and interpolation techniques to obtain the schemes. Direct form of power series is used as basis function for approximation solution. An order eight symmetric and zero-stable method is obtained. To implement our method, predictors of the same order of accuracy as the main method were developed using Taylor’s series algorithm. This implementation strategy is found to be efficient and more accurate as the result has shown in the numerical experiments. The result obtained confirmed the superiority of our method over existing methods.
Year
Volume
118
Pages
236-250
Physical description
Contributors
  • Department of Mathematics, Ambrose Alli University, Ekpoma, Edo State, Nigeria
  • Department of Mathematics & Statistics, Joseph Ayo Babalola University, Osun State, Nigeria
References
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  • [4] Awoyemi, D.O, Algorithmic collocation methods for the direct solution of special and general fourth order initial value problems in ordinary differential equations. Inter. Journal of Computer Math. vol. 6, (2001) 271-218.
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  • [6] Awoyemi, D.O. and Kayode, S.J, An optimal order continuous multistep algorithm for initial value of special second order differential equations. Journal of the Nigeria Assocition of Mathematical Physics, vol. 6, (2002) 285-292.
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  • [8] Kayode, S.J. and Awoyemi, D.O, A 5-step maximal order method for the direct solution of second order ordinary differential equations, Journal of the Nigerian Association of Mathematical Physics, vol. 4, (2005) 279-284.
  • [9] Anake, T.A., Awoyemi, D.O and Adesanya, A.O, A one-step method for the solution of general second order ordinary differential equations. Inter Journal of Science and Technology, 2(4); (2012) 159-163.
  • [10] Adesanya, A.O, Block Methods for the solution of higher order initial value problems in ordinary differential equations .Ph.D Thesis (unpublished), Federal University of Technology, Akure, Nigeria (2011)
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  • [16] Olabode, B.T. and Alabi. T.J, Direct Block Predictor- Corrector Methods for the solution of General Fourth Order ODEs. Journal of Mathematics Research, vol. 5(1), (2013) 26-33
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Document Type
article
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjd-273f6f93-20ca-45e9-86f4-dd22174894e5
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