DISCRETIZATION OF SOLUTIONS TO THE HEAT EQUATION IN THE CONTEXT OF THE STUDY "СOMPUTATIONAL (NUMERICAL) DIAMETER" - Utessova, Г.И.; Utessov, А.Б. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2022)
In many cases, solutions to partial differential equations are represented by series or integrals, which are infinite objects. Therefore, the problem of approximation (discretization) of solutions of differential equations with partial derivatives, represented by series or integrals, arises. In this work, according to the research scheme called "Сomputational (numerical) diameter " in the metric of space , we solve the problem of discretization of solutions (represented by multiple series) of the heat equation with an initial condition from the functional class by computing units constructed from the values of linear functionals defined on the class Namely, firstly, the exact order of discretization of the solution is established and a computing unit is proposed that implements the established exact order; secondly, the limiting error of the proposed computing unit was found; thirdly, it has been proved that the limiting error of any computing unit constructed from the trigonometric Fourier coefficients of the initial condition is no better in order than the limiting error of the proposed computing unit.