OPTIMAL APPROXIMATION OF SOLUTIONS OF POISSON EQUATION BY INITIAL DATA IN THE FORM OF ACCURATE AND INACCURATE INFORMATION OF TRIGONOMETRIC FOURIER COEFFICIENTS
Arystangalikyzy A. Zhubanysheva A.Zh.
30 September 2025al-Farabi Kazakh State National University
KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2025#127Issue 311 - 25 pp.
Partial differential equations along with a function, derivative, and integral are basic mathematical models. Therefore, the problem of their approximation by accurate and inaccurate information with the construction of optimal computational aggregates (approximation methods) of approximation is relevant and many articles are devoted to this issue. In the article is considered the problem of approximation of solutions of Poisson equation with the right-hand side f from the Nikol’skii classes H2r (0, 1)s in the Lebesgue metrics L2 (0, 1)s and L∞ (0, 1)s . The orders of error of approximation of solutions of the Poisson equation by accurate and inaccurate information in the form of trigonometric Fourier coefficients of f are obtained. Namely, a lower bound for the approximation error based on accurate information is found for all possible computational agregates using an arbitrary finite set of trigonometric Fourier coefficients. A computational agregate (approximation method) by the trigonometric Fourier coefficients of the right-hand side f of the equation is constructed that confirms this lower bound. The boundaries of ˜εN of inaccurate information preserving the order of error of approximation by accurate information are established.
approximation by accurate and inaccurate information , boundaries of inaccurate information , Nikol’skii classes , optimal computational aggregate , Poisson equation
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K. Zhubanov Aktobe Regional University, Aktobe, Kazakhstan
L. N. Gumilyov Eurasian National University, Astana, Kazakhstan
K. Zhubanov Aktobe Regional University
L. N. Gumilyov Eurasian National University
10 лет помогаем публиковать статьи Международный издатель
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