O.A. Dmitrieva

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The paper concerns itself with the numerical realization of the Cauchy problem for ordinary differential equations and their systems in parallel computer systems. The block collocation methods are developed that allow us to find a solution simultaneously in all the calculating points of the block, which reduces the time of obtaining the solution even for the sequential implementation. In order to align the order of approximation in all the calculating points of the block the additional higher-order derivatives are introduced into the difference schemes. The conditions of stability, the order of accuracy and the convergence of the initial data and of the right-hand side are determined for the developed methods. It is shown that the order of approximation of the introduced methods is much higher than that of classical models, and the same in all calculating points of the block.