Solving systems of differential equations of block structure with nonseparated boundary conditions

Abstract

We study the solution of a system of higher-dimensional ordinary differential equations of block structure. Some separate subsystems are connected with each other by the nonseparated boundary conditions caused by an arbitrary relation between the boundary values of the solutions to the subsystems. For numerical solution, we propose some scheme of the method of transferring the boundary conditions that takes into account the specific characteristics of the systems under consideration. The results of numerical experiments are given. DOI: 10.1134/S1990478915010019 In this article, taking into account the block structure of the system of differential equations and the weak but arbitrary filling of the boundary condition matrix, we propose a version of the method of transfer of the boundary conditions. The advantage of this approach in comparison with the direct use of transfer methods in general form is obvious since here the transfer is carried out only with respect to those variables whose coefficients in the boundary conditions are nonzero; moreover, the transfer is carried out with the use of the only subsystem of differential equations involving the variable that is being transferred. We show the results of the numerical experiments obtained by solving a test problem based on the problem of calculating an unsteady fluid motion in a fragment of a pipeline network of complex structure.