A Fifth-fourth Continuous Block Implicit Hybrid Method for the Solution of Third Order Initial Value Problems in Ordinary Differential Equations
Applied and Computational Mathematics
Volume 8, Issue 3, June 2019, Pages: 50-57
Received: Jan. 30, 2019; Accepted: Mar. 17, 2019; Published: Aug. 12, 2019
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Authors
Adoghe Lawrence Osa, Department of Mathematics, Ambrose Alli University, Ekpoma, Edo State, Nigeria
Omole Ezekiel Olaoluwa, Department of Mathematics, Federal University of Technology, Akure, Nigeria
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Abstract
In this paper, block method was developed using method of collocation and interpolation of power series as approximate solution to give a system of non linear equations which is solved to give a continuous hybrid linear multistep method. The continuous hybrid linear multistep method is solved for the independent solutions to give a continuous hybrid block method which is then evaluated at some selected grid points to give a discrete block method. The basic properties of the discrete block method were investigated and found to be zero stable, consistent and convergent. The derived scheme was tested on some numerical examples and was found to give better approximation than the existing method.
Keywords
Collocation, Interpolation, Approximate Solution, Continuous Block Method, Discrete Block Method, Convergence
To cite this article
Adoghe Lawrence Osa, Omole Ezekiel Olaoluwa, A Fifth-fourth Continuous Block Implicit Hybrid Method for the Solution of Third Order Initial Value Problems in Ordinary Differential Equations, Applied and Computational Mathematics. Vol. 8, No. 3, 2019, pp. 50-57. doi: 10.11648/j.acm.20190803.11
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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