论求解泊松方程的离散化算子的误差估计值

IF 0.8 4区数学 Q2 MATHEMATICS Differential Equations Pub Date : 2024-04-09 DOI:10.1134/s0012266124010117

A. B. Utesov

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引用次数: 0

摘要

Abstract 从 Korobov 类中构造了波松方程右边解的离散化算子，并在\(L^{p} \)度量中估计了其误差，\(2\leq p\leq \infty \)。结果证明，对于（p=2），离散化运算符的误差估计在幂级数上是尖锐的。计算离散化算子时使用的三角傅里叶系数时也发现了误差。值得注意的是，在一种情况下，所得到的估计值优于之前已知的根据修正的 Korobov 网格和 Smolyak 网格节点处方程右侧值构建的离散化算子误差估计值，而在另一种情况下，它与它们重合到常数。

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On Error Estimates for Discretization Operators for the Solution of the Poisson Equation

Abstract

A discretization operator for the solution of the Poisson equation with the right-hand side from the Korobov class is constructed and its error is estimated in the \(L^{p} \)-metric, \(2\leq p\leq \infty \). It is proved that for \(p=2 \) the resulting error estimate for the discretization operator is order sharp on the power scale. An error in calculating the trigonometric Fourier coefficients used when constructing the discretization operator is also found. It should be noted that the obtained estimate in one case is better than previously known estimates of the errors of discretization operators constructed from the values of the right-hand side of the equation at the nodes of the modified Korobov grid and the Smolyak grid, and in the other case it coincides with them up to constants.

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.