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In the numerical solution of differential equations, the continuous domain of solutions of DU is replaced by a discrete lattice, at the nodes of which the value of the unknown function is approximately computed. In the zone of shock waves, interphase boundaries and boundary layers with the use of regular grids, there can be a sharp increase in the norm of the derivatives and as a consequence of the standard of approximation errors, which leads to a loss of the accuracy of the numerical solution. To suppress the growth of approximation errors, adaptive algorithms for thickening grids in problem areas are used. The paper briefly describes the approach to parallelizing such an algorithm based on the concept of dynamic parallelization "T-system".