Analiz mnogotochechnoy kraevoy zadachi dlya nelineynogo matrichnogo differentsial'nogo uravneniya

Abstract

For a nonlinear differential matrix equation, we study a multipoint boundary valueproblem by a constructive method of regularization over the linear part of the equation usingthe corresponding fundamental matrices. Based on the initial data of the problem, sufficientconditions for its unique solvability are obtained. Iterative algorithms containing relativelysimple computational procedures are proposed for constructing a solution. Effective estimatesare given that characterize the rate of convergence of the iteration sequence to the solution, aswell as estimates of the solution localization domain.