ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

The Improvement of Numerical Solutions of Ordinary Differential Equations by Genetic Transforms


Vladimir Nikolaevich Taran

Don State Technical University,
Technological Institute (branch) of DSTU in Azov, Rostov region, Azov
Professor, Doctor of Physical and Mathematical Sciences

Artem Mihailovich Dolzhenko

Don State Technical University,
Technological Institute (branch) of DSTU in Azov, Rostov region, Azov

Kristina Kyastuchio Rybalko

Don State Technical University,
Technological Institute (branch) of DSTU in Azov, Rostov region, Azov


The article describes the modified genetic algorithm for the Cauchy problem solving. To analyze the method effectiveness we perform series of tests which results are presented in tables and figures.The comparison of solutions obtained by the offered method and classical ones (Runge-Kutta and Adams-Bachfort) has been done. The input parameters of the algorithm which give the most accurate result are determined. The application of the algorithm to the problems which do not have the analytical solution is shown. Scientific novelty of the work consists in the realization of a new numerical method for solving ordinary differential equations, which has higher class of accuracy than classical methods. The analysis of scientific works in a scope of genetic algorithms has shown that the authors method of refinement numerical solutions by genetic algorithms is unique and has not been previously described. Relevance of the method is caused by the possibility to apply the offered approach to a modification of a wide class of numerical algorithms solutions.



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