FEATURES OF THE NUMERICAL SOLUTION OF BOUNDARY VALUE PROBLEMS WITH THE USE OF PYTHON ALGORITHMIC PROGRAMMING LANGUAGE

Abstract

The solution of the majority of the practical tasks arising at calculation of constructions demands a numerical solution of boundary value problems. In article on examples of a solution of specific boundary value problems possibilities of a modern object-oriented programming language of Python are described. This lan-guage possesses convenient syntax and opportunities of flexible use of the existing libraries of the numerical methods allowing the user to prepare a program code and to start studying of a task in the shortest terms. Rich opportunities of graphic library Matplotlib are allowed to have graphic display of results of calculation. The Numpy library used in article is standard library for carrying out any matrix and vector calculations in the Python language, its application turns the Python language on Wednesday for programming of numerical calculations, similar to such widely known software products as Matlab and GNU Octave. In article the method of finite differences has solved a task for Laplace's equation, the describing field distribution of temperature on rectangular area; problem of search of a minimum of functionality of Dirikhle by a variational-difference method; a dy-namic problem of vibration of weight on a visco-elastic element at vibrations of the basis and a three-dimensional task of the theory of elasticity by a variational-difference method.

Keywords

• variational-difference method of a solution of boundary value problems, Python programming language, three-dimensional boundary value problem of the theory of elasticity, search of a minimum of functionality of Dirikhle