双调和方程组积分方程的快速傅立叶-伽辽金方法

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Integral Equations and Applications Pub Date : 2021-12-01 DOI:10.1216/jie.2021.33.511

Bo Wang, D. Yu, Bao Tan

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引用次数: 0

摘要

本文给出了求解一类积分方程组的快速傅立叶-伽辽金方法，该方法是双调和方程的狄利克雷问题的一种重新表述。该方法基于算子分割和截断策略设计。截断后的矩阵只有O(n log n)个非零项，但近似解保持了稳定性和最优收敛阶。数值算例验证了理论估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A fast Fourier–Galerkin method solving a system of integral equations for the biharmonic equation

In this paper, a fast Fourier-Galerkin method is presented for solving a system of integral equations, which is a reformulation of the Dirichlet problem of the biharmonic equation. This method is based on operator splitting and truncation strategy designing. The truncated matrix has only O(n log n) nonzero entries, but the approximate solutions preserve the stability and optimal convergence order. Numerical examples indicate the theoretical estimate.

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来源期刊

Journal of Integral Equations and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Integral Equations and Applications is an international journal devoted to research in the general area of integral equations and their applications. The Journal of Integral Equations and Applications, founded in 1988, endeavors to publish significant research papers and substantial expository/survey papers in theory, numerical analysis, and applications of various areas of integral equations, and to influence and shape developments in this field. The Editors aim at maintaining a balanced coverage between theory and applications, between existence theory and constructive approximation, and between topological/operator-theoretic methods and classical methods in all types of integral equations. The journal is expected to be an excellent source of current information in this area for mathematicians, numerical analysts, engineers, physicists, biologists and other users of integral equations in the applied mathematical sciences.