Calculation of a state of the system of discrete linear processes connected by nonseparated boundary conditions

We propose some approach to solving a collection of linear discrete block-diagonal systems with boundary conditions not separated between the blocks. Using the peculiarities of the structure of the system, we obtain formulas for the transfer of the values of the initial and final variables in the boundary conditions which is carried out in each of the blocks independently. The result is an algebraic system whose dimension is determined by the number of blocks and the unknowns are only those of the initial or final variables of each of the blocks. The results are given of the numerical solution of the problem which uses the finite-difference approximation method to the calculation of the transitional regimes of the motion of a fluid in pipelines of complex structure are given.