Authors A.M. Onishkova
Month, Year 01, 2013 @en
Index UDC 519.688+519.63
Abstract The study of many problems in mathematical physics reduces to the solution of boundary value problems with an unknown or a free interface. The solution of such tasks is associated with some difficulties. The purpose is to find the solution of this problem, that is the definition of an unknown interface. Determine the solution is often possible only numerically using variational methods. In this work The numerical algorithm consists of in determination of a minimum of some quadratic functional, defined in the area containing in advance unknown interfaces. The unknown interface is obtained from a minimisation condition of the functional together with unknown functions. The problem for plane area dares a method of grids. The presented new algorithm uses various methods to search minimum, in particular, genetic algorithms are implemented. The results of numerical experiments are presented. From the results it is concluded that we have a new algorithm to search the unknown interfaces for two-dimensional problem, the advantage of which is the combination of the variational approach to finding the unknown interface and genetic algorithms to search for a local minimum in terms of having multiple minimizers.

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Keywords Algorithm; functional; minimum; genetic algorithm; grid; function; area; interface.
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