Methods of composition of different approximations in the simulation of dynamic processes

The paper investigates methods of composing difference approximations for forming single- and multi-step parallel difference schemes of a given order, oriented to the numerical solution of the Cauchy problem for both ordinary differential equations and evolutionary partial differential equations. The proposed discrete approximations allow us to vary the order of the error, departing from the maximum possible on a fixed set of nodes, but ensuring absolute or A-α stability of numerical solutions. The study of the properties of the proposed transition matrices connecting the reference and design points allows us to determine the nature of the stability of the generated difference schemes according to the initial data and the right-hand sides. Automatic generation of stable difference schemes allows taking into account the topology of the processor field, and thus, using the available computing resource with maximum efficiency. Figs.: 10. Refs.: 18 titles.