Модификация алгоритмов метода параметризации Джумабаева и численный метод

Abstract

The article deals with a modification of the algorithms of D. S. Dzhumabaev's paramet-rization method. Additional parameters are introduced at the internal partition points and at both ends of the interval. Sufficient conditions for convergence of these algorithms in terms of input data are given. Using the right-hand part of the system of differential equations and the boundary condition function, a nonlinear operator equation was constructed to find initial approximations of unknown parameters. A numerical method is proposed for finding a solution to a nonlinear two-point boundary value problem for a system of ordinary differential equations. The numerical method was implemented in a test example.