变系数非线性二阶问题有效的Fourier谱逼近
Efficient Fourier Spectral Approximation for Nonlinear Second-Order Problems with Variable Coefficients
摘要: 本文针对周期边界条件下变系数非线性二阶问题提出了一种有效的Fourier谱方法。首先，根据边界条件引入了适当的Sobolev空间及其逼近空间，建立了变系数非线性二阶问题的弱形式和相应的离散格式。基于这非线性的离散格式，我们建立了一种线性迭代算法，并给出了该算法相应的Matlab程序设计。最后，我们给出了数值算例，数值结果表明我们提出的算法是收敛的和高精度的。
Abstract: In this paper, an efficient Fourier spectral method is proposed for nonlinear second-order problems with variable coefficients under periodic boundary conditions. Firstly, an appropriate Sobolev space and its approximation space are introduced according to the boundary conditions, and the weak form and the corresponding discrete scheme of the nonlinear second-order problem with variable coefficients are established. Based on the nonlinear discrete scheme, we establish a linear iterative algorithm and its Matlab program design. Finally, we give a numerical example, and the numerical results show that our proposed algorithm is convergent and highly accurate.
文章引用：江婷婷. 变系数非线性二阶问题有效的Fourier谱逼近[J]. 应用数学进展, 2022, 11(7): 4268-4277. https://doi.org/10.12677/AAM.2022.117453

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