Approximate solutions of general second–order initial value problems using differential evolution
Abstract
In this paper, it is assumed that the solution of the general second order initial value problem $u^{\prime \prime} = f\left(t, u, u^{\prime} \right);\quad u(t_0) = u_0,\;\;u^{\prime}(t_0) = u^{\prime}_0, \quad t \in \left[t_0,t_n\right]$ can be approximated by a polynomial \emph{u(t)}. To obtain the values of the coefficients of the terms of \emph{u(t)}, the problem is converted to an optimization problem and the simple stochastic function minimizer called differential evolution is used to obtain the optimal values of the coefficients. Numerical examples show the efficiency and accuracy of the proposed technique compared with some existing classical methods.
Copyright © 2017 Omolara Fatimah Bakre, Ashiribo Senapon Wusu, Moses Adebowale Akanbi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
O. F. Bakre, A. S. Wusu, M. A. Akanbi, Approximate solutions of general second–order initial value problems using differential evolution, J. Math. Comput. Sci. 7 (2017), 966–972.
BibTeX
@article{Bakre2017,
author = {Bakre, Omolara Fatimah and Wusu, Ashiribo Senapon and Akanbi, Moses Adebowale},
title = {Approximate solutions of general second–order initial value problems using differential evolution},
journal = {J. Math. Comput. Sci.},
volume = {7},
year = {2017},
pages = {966--972},
doi = {}
}