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

Abstract

We propose some approach to solving a set of discrete block-diagonal linear systems with boundary conditions unseparated between the blocks. Using the specificity of the system structure, some formulas are obtained for transferring the values of initial and final variables in the boundary conditions which is carried out independently in each block. The result is an algebraic system whose dimension is determined by the number of blocks, while the unknowns are just the values of initial or final variables of all blocks. The numerical results are shown for the problem obtained by application of the method of finite-difference approximation to calculation of transient regimes of a fluid flow in pipelines of a complex structure.