Description: The paper discusses approaches focused on the numerical simulation of dynamic systems with lumped parameters. In order to enable the parallel implementation the modification of the classical methods of Bickart type with one advanced point has been proposed, which allows one to increase the number of calculation points, forming the calculation bock. For the developed difference schemes the systems of equations have been built, which allow one to determine the calculation coefficients for any dimension of the block. The absolute stability of the developed methods on the initial data and the conditional stability on the right-hand side have been proved. The dependence of the stability on the right-hand side on the number of calculation points in a block has been studied. Parallel implementation of the developed methods has been carried out on well-known test problems with an arbitrary dimension with introducing into simulation algorithms the procedure of integration step control.
Keywords: the Cauchy problem, the Bickart method, a block method, a difference scheme, the stability domain, the integration step, the transition matrix