ON DISCRETIZATION OF SOLUTIONS OF THE HEAT EQUATION BY NUMERICAL INFORMATION - Utessov А.; Utessova Г. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2022)
Solutions to many partial differential equations are represented by series or integrals. Therefore, theproblemarises of approximating (discretizing) solutions by computational units constructed from numerical information obtained from the initial, boundary or boundary conditions. In this paper, within the framework of a statement titled “Computational (numerical) diameter”, we study the discretization problem for solutions of the heat equation from numerical information of a finite volume obtained from an initial condition belonging to the multidimensional periodic Sobolev class. Namely, when linear functionals defined on the linear hull of the Sobolev class are considered as numerical information, first, the exact order of the error of optimal discretization in the metric of the Lebesgue space is established; secondly, the limiting error of the optimal computing unit is found; thirdly, it is provided that there is no initial condition with the best (in order) limiting error of computational aggregates in terms of trigonometric Fourier coefficients.