Vakal L. Using of chebyshev approximations for solving of some problems of mathematical modeling and mathematical physics.

The thesis is devoted to development of methods and algorithms for mathematical modeling of experimental data and for solving of some boundary value problems and Fredholm integral equations with using of uniform approximations. It is proposed a method and an algorithm for uniform piecewise polynomial approximation with optimal knots and advanced an algorithm for the best uniform approximation of many-variables functions by generalized polynomials. To approximate experimental data they are created algorithms for uniform approximation by nonlinear function with two and three parameters. For solving of Fredholm linear integral equations it is developed a method of maximum integral residual minimization. It is also proposed to use the best uniform approximation by generalized polynomials of two variables in the method of an integral kernal replacing by a degenerate kernel. To solve linear boundary value problems and initial-boundary problems for differential equation it is proposed a method based on using the best uniform approximation of functions and realized by minimization of maximum differential residual, approximation of boundary conditions, approximation of initial conditions. The method permits to find more precise solutions and to receive estimations of their accuracy.