Аңдатпа
Abstract This paper investigates the exact orders of approximation of solutions to the Cauchy problem for the heat equation when the available information is inaccurate. The study identifies the optimal computational aggregates that achieve these approximation orders. The inaccuracy in the data arises from the Fourier coefficients of the initial condition, which belongs to the Nikol’skii–Besov class. The limiting error of the inaccurate information of computational aggregates constructed from Fourier coefficients with an arbitrary finite spectrum, is also determined. Furthermore, a set of computational aggregates is constructed, each having a limiting error not greater than the limiting error established in the C(N)D-2 problem. Numerical experiments have been carried out, confirming the theoretical results.