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OJOp> Vol.4 No.3, September 2015
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Solving Ordinary Differential Equations with Evolutionary Algorithms

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DOI: 10.4236/ojop.2015.43009    3,531 Downloads   4,312 Views   Citations
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Bakre Omolara Fatimah1, Wusu Ashiribo Senapon2, Akanbi Moses Adebowale2

Affiliation(s)

1Department of Mathematics, Federal College of Education (Technical), Lagos, Nigeria.
2Department of Mathematics, Lagos State University, Lagos, Nigeria.

ABSTRACT

In this paper, the authors show that the general linear second order ordinary Differential Equation can be formulated as an optimization problem and that evolutionary algorithms for solving optimization problems can also be adapted for solving the formulated problem. The authors propose a polynomial based scheme for achieving the above objectives. The coefficients of the proposed scheme are approximated by an evolutionary algorithm known as Differential Evolution (DE). Numerical examples with good results show the accuracy of the proposed method compared with some existing methods.

KEYWORDS

Evolutionary Algorithm, Differential Equations, Differential Evolution, Optimization

Cite this paper

Fatimah, B. , Senapon, W. and Adebowale, A. (2015) Solving Ordinary Differential Equations with Evolutionary Algorithms. Open Journal of Optimization, 4, 69-73. doi: 10.4236/ojop.2015.43009.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Buctcher, J.C. (2008) Numerical Methods for Ordinary Differential Equations. Wiley, New York.
http://dx.doi.org/10.1002/9780470753767
[2] Lambert, J.D. (1973) Computational Methods in ODEs. Wiley, New York.
[3] Lambert, J.D. (1991) Numerical Methods for Ordinary Differential Systems. Wiley, New York.
[4] Goldberg, D.E. (1989) Genetic Algorithms in Search, Optimization and Machine Learning. 2nd Edition, Addison- Wesley, Boston.
[5] Holland, H.J. (1975) Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor.
[6] Mastorakis, N.E. (2006) Unstable Ordinary Differential Equations: Solution via Genetic Algorithms and the Method of Nelder-Mead. Proceedings of the 6th WSEAS International Conference on Systems Theory & Scientific Computation, Elounda, 21-23 August 2006, 1-6.
[7] Michalewiz, Z. (1994) Genetic Algorithm + Data Structure = Evolution Programs. 2nd Edition, Springer-Verlag, Berlin.
http://dx.doi.org/10.1007/978-3-662-07418-3
[8] Mastorakis, N.E. (2005) Numerical Solution of Non-Linear Ordinary Differential Equations via Collocation Method (Finite Elements) and Genetic Algorithms. Proceedings of the 6th WSEAS International Conference on Evolutionary Computing, Lisbon, 16-18 June 2005, 36-42.
[9] Junaid, A., Raja, A.Z. and Qureshi, I.M. (2009) Evolutionary Computing Approach for the Solution of Initial Value Problems in Ordinary Diffential Equations. International Scholarly and Scientific Research & Innovation, 3, 516-519.
[10] George, D.M. (2006) On the Application of Genetic Algorithms to Differential Equations. Romanian Journal of Economic Forecasting, 2, 5-9.

  
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