Introduction of an irregular grid with respect to the spatial coordinate for the method of lines

Abstract

The paper deals with the problem of reducing evolutionary partial differential equations to systems of ordinary differential equations with discretization over space. It is assumed that the obtained systems will be implemented iparallel using the method of lines. The questions devoted to the parallel control of the step of time integration on the basis of collocation block methods are considered. For the spatial coordinate, an irregular grid with a Chebyshev arrangement of nodes is introduced, which makes it possible to improve the accuracy of the results without significantl y increasing the computational complexity. The obtained results are confirmed by computer experiments for partial parabolic partial di fferential equations with different types of boundary condi tions and stiffness parameters.