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Тезисы докладов

Аппроксимация функций и квадратурные формулы

The techniques of construction of orthogonal compactly supported functions [1] are considered. The functions have one, two, three and more arguments. The examples of such functions on grids are resulted, the grids consist of rectangulars, triangles and tetrahedrons. The comparison of functions with wavelets shows advantages of offered functions at their use in numerical methods. The approximations in functional spaces constructed with the help of these functions are investigated. The numerical methods [2] of mathematical physics and mechanics of deformable bodies are considered. The methods are based on the mixed variational principles and use orthogonal compactly supported functions. The application of methods in tasks of the theory of bars, plates, in spectral tasks is considered. The convergence of methods in tasks of mathematical physics, theory of bars, theory of plates, theory of elasticity is proved. The results of accounts on the computer show efficiency of methods in tasks of a statics and dynamics of elastic bodies. 1. V.L.Leont'ev, N.Ch.Lukashanets, Grid Bases of Orthogonal Compactly Supported Functions // Computational Mathematics and Mathematical Physics, Vol. 39, No. 7, 1999, pp. 1116-1126. 2. V.L.Leont'ev, Orthogonal Compactly Supported Functions in Eigenvalue Problems // Computational Mathematics and Mathematical Physics, Vo. 41, No. 6, 2001, pp. 825 - 831.

Примечание. Тезисы докладов публикуются в авторской редакции

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