2021 A fast Fourier–Galerkin method solving a system of integral equations for the biharmonic equation
Bo Wang, Dandan Yu, Bao Tan
J. Integral Equations Applications 33(4): 511-530 (2021). DOI: 10.1216/jie.2021.33.511

Abstract

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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Bo Wang. Dandan Yu. Bao Tan. "A fast Fourier–Galerkin method solving a system of integral equations for the biharmonic equation." J. Integral Equations Applications 33 (4) 511 - 530, 2021. https://doi.org/10.1216/jie.2021.33.511

Information

Received: 17 February 2021; Revised: 10 April 2021; Accepted: 13 April 2021; Published: 2021
First available in Project Euclid: 11 March 2022

MathSciNet: MR4393382
zbMATH: 1495.31009
Digital Object Identifier: 10.1216/jie.2021.33.511

Subjects:
Primary: 31A30 , 45E05 , 74S25

Keywords: Biharmonic equation , boundary integral equation , Dirichlet problem , fast Fourier–Galerkin methods

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.33 • No. 4 • 2021
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