GENERATION OF THE TRANSITION OPERATOR FOR PARALLEL STEP CONTROL AT MODELING LINEAR DYNAMIC SYSTEMS

Abstract

Parallel algorithms of modeling of the linear dynamic objects based on the construction of transition operators are offered. The developed algorithms are based on the nested stages schemes and allow one to fulfill an automatic selection of the optimum step size at each grid point. Parallel realization is focused on the cluster computing systems of type MIMD. The basic idea, which is based on the construction of the transition operators for solving linear systems of ordinary differential equations on parallel computers, is the simultaneous receipt of two approximations of different orders. Step control algorithms proposed in the article are based on the use of nested stages methods. Parallel processing is carried out within each step with the number of stages s and s+1. Two strands of calculations are independent and need to exchange occurs only after the final results for the calculation points. Transition operators for each s-stage method are built once, before the calculations and allow reducing the number of matrix operations performed at each step by s times due to parallel implementation.