Ordinary differential equations Cauchy problem solving with genetic programming techniques
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 1, pp. 61-69
Cet article a éte moissonné depuis la source Math-Net.Ru
It is suggested to use genetic programming techniques for solving Cauchy problem that allows to get exact analytical solution if it does exist and approximate analytical expression otherwise. Features of solving process with this approach are considered. Results of numerical experiments are given.
Keywords:
ordinary differential equations, Cauchy problem, numeric methods, genetic programming algorithm.
@article{JSFU_2011_4_1_a6,
author = {Sergey F. Burakov and Evgeny S. Semenkin},
title = {Ordinary differential equations {Cauchy} problem solving with genetic programming techniques},
journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
pages = {61--69},
year = {2011},
volume = {4},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/JSFU_2011_4_1_a6/}
}
TY - JOUR AU - Sergey F. Burakov AU - Evgeny S. Semenkin TI - Ordinary differential equations Cauchy problem solving with genetic programming techniques JO - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika PY - 2011 SP - 61 EP - 69 VL - 4 IS - 1 UR - http://geodesic.mathdoc.fr/item/JSFU_2011_4_1_a6/ LA - ru ID - JSFU_2011_4_1_a6 ER -
%0 Journal Article %A Sergey F. Burakov %A Evgeny S. Semenkin %T Ordinary differential equations Cauchy problem solving with genetic programming techniques %J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika %D 2011 %P 61-69 %V 4 %N 1 %U http://geodesic.mathdoc.fr/item/JSFU_2011_4_1_a6/ %G ru %F JSFU_2011_4_1_a6
Sergey F. Burakov; Evgeny S. Semenkin. Ordinary differential equations Cauchy problem solving with genetic programming techniques. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 1, pp. 61-69. http://geodesic.mathdoc.fr/item/JSFU_2011_4_1_a6/
[1] I. G. Petrovskii, Lektsii po teorii obyknovennykh differentsialnykh uravnenii, MGU, M., 1984 | MR
[2] A. A. Samarskii, Teoriya raznostnykh skhem, Nauka, M., 1989 | MR
[3] J. R. Koza, Genetic Programming, On Programming Computer by Means of Natural Selection and Genetics, The MIT Press, Cambridge, MA, 1992, 51–62
[4] B. Bandi, Metody optimizatsii (vvodnyi kurs), Radio i svyaz, M., 1988
[5] A. F. Filippov, Sbornik zadach po differentsialnym uravneniyam, NITs “Regulyarnaya i khaoticheskaya dinamika”, Moskva–Izhevsk, 2003