周期边界条件下四阶特征值问题的一种有效的 Fourier 谱逼近

Abstract

Abstract:

In this paper, we put forward an effective Fourier spectral approximation method for fourth-order eigenvalue problems with periodic boundary conditions. Firstly, we introduce the appropriate Sobolev space and the corresponding approximation space according to the periodic boundary conditions, establish a weak form of the original problem and its discrete form, and derive the equivalent operator form. Then we define an orthogonal projection operator and prove its approximation properties. Combined with the spectral theory of compact operators, we prove the error estimates of approximation eigenvalues. In addition, we construct a set of basis functions of the approximation space, and derive the matrix form based on tensor product associated with the discrete scheme. Finally, we provide some numerical examples, and the numerical results show our algorithm is effective and spectral accuracy.

Key words: Periodic boundary, Fourth-order eigenvalue problem, Fourier spectral method, Error estimates

CLC Number:

O241.82

He Ya, An Jing. An Effective Fourier Spectral Approximation for Fourth-Order Eigenvalue Problems with Periodic Boundary Conditions[J].Acta mathematica scientia,Series A, 2024, 44(1): 37-49.

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An Effective Fourier Spectral Approximation for Fourth-Order Eigenvalue Problems with Periodic Boundary Conditions

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