Unstable ordinary differential equations: Solution via genetic algorithms and the method of Nelder-Mead

WSEAS Transactions on Mathematics

Volumn 5, Issue 12, 2006, Pages 1276-1281

  Mastorakis, Nikos E ^a,b  

^a World Scientific Engineering Academy and Society   (Greece)

^b HELLENIC NAVAL ACADEMY   (Greece)

Author keywords

Genetic algorithms; Numerical solutions; Unstable differential equations

Indexed keywords

COMPUTATIONAL METHODS; GENETIC ALGORITHMS; NUMERICAL METHODS;

COMPUTATIONAL SCHEME; NELDER-MEAD METHOD; NUMERICAL SOLUTIONS;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 33751566122     PISSN: 11092769     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. Nikos E. Mastorakis, "Solving Differential Equations via Genetic Algorithms", Proceedings of the Circuits, Systems and Computers '96 (CSC'96), Piraeus, Greece, July 15-17, 1996, 3rd Volume: Appendix, pp.733-737
2. Nikos E. Mastorakis, "On the Solution of III-Conditioned Systems of Linear and Non-Linear Equations via Genetic Algorithms (GAs) and Nelder-Mead Simplex Searchs", Proceedings of the 6th WSEAS International Conference on Evolutionary Computing, Lisbon, Portugal, June 16-18, 2005.
3. Goldberg D.E. (1989), Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Second Edition, 1989
4. Ralf Östermark, "Solving Irregular Econometric and Mathematical Optimization Problems with a Genetic Hybrid Algorithm", Computational Economics, Volume 13, Issue 2, pp. 103-115, April 1999.
5. Lagarias, J.C., J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM Journal of Optimization, Vol. 9 Number 1, pp. 112-147, 1998.
6. J. A. Nelder and R. Mead, "A simplex method for function minimization", Computer Journal, 7, 308-313, 1965
7. F. H. Walters, L. R. Parker, S. L. Morgan, and S. N. Deming, Sequential Simplex Optimization, CRC Press, Boca Raton, FL, 1991.
8. Matlab, Version 7.0.0, by Math Works, Natick, MA, 1994 http://www.mathworks.com
9. E. Balagusuramy, Numerical Methods, Tata McGraw Hill, New Delhi, 1999
10. Gonos I.F., Mastorakis N.E., Swamy M.N.S.: "A Genetic Algorithm Approach to the Problem of Factorization of General Multidimensional Polynomials", IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Part I, Vol. 50, No. 1, pp. 16-22, January 2003.
11. Mastorakis N.E., Gonos I.F., Swamy M.N.S.: "Design of 2-Dimensional Recursive Filters using Genetic Algorithms", IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Part I, Vol. 50, No. 5, pp. 634-639, May 2003.
12. Mastorakis N.E., Gonos I.F., Swamy M.N.S.: "Stability of Multidimensional Systems using Genetic Algorithms", IEEE Transactions on Circuits and Systems, Part I, Vol. 50, No. 7, pp. 962-965, July 2003.