Abstract
We obtain the exact order of discretization (reconstruction) errors, given linear information on the solutions of the heat equation.
Similar content being viewed by others
References
N. Temirgaliev, “Number-theoretic methods and the probability-theoretic approach problems of calculus. Embeddings and approximation theory, absolute convergence, and Fourier series transformation,” Vestnik Eurasian Univ., No. 3, 90–144 (1997).
N. Temirgaliev, “Number-theoretic methods and the probability-theoretic approach problems of calculus. Embeddings and approximation theory, absolute convergence, and Fourier series transformation,” (Sequel 1),” Vestnik Eurasian Univ., No. 3–4, 222–272 (2002).
N. M. Korobov, Number-Theoretic Methods in Approximate Analysis (Fizmatgiz, Moscow, 1963) [in Russian].
S. A. Smolyak, “Quadrature and interpolation formulas on tensor products for some classes of functions,” Dokl.Akad. Nauk SSSR 148(5), 1042–1045 (1963).
Loo Keng Hua and Yang Wang, Application of Number Theory to Numerical Analysis (Springer-Verlag, Berlin-Heidelberg-New York, 1981).
K. E. Sherniyazov, Approximate Reconstruction of Functions and Solutions of the Heat Equation with Distribution Functions of Initial Temperatures from the Classes E, SW, and B, Cand. Sci. (Phys.- Math.) Dissertation (Al Farabi Kazakh State Univ. Almaty, 1998)[in Russian].
S. M. Nikol’skii, Approximation of Functions of Several Variables and Embedding Theorems (Nauka, Moscow, 1977) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Azhgaliev, S. Discretization of the solutions of the heat equation. Math Notes 82, 153–158 (2007). https://doi.org/10.1134/S000143460707019X
Received:
Issue Date:
DOI: https://doi.org/10.1134/S000143460707019X