确定 Korteweg-de Vries 方程中的未知系数

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Inverse and Ill-Posed Problems Pub Date : 2024-06-25 DOI:10.1515/jiip-2024-0008

Lin Sang, Yan Qiao, Hua Wu

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引用次数: 0

摘要

本文研究了一种求解 Korteweg-de Vries 方程逆问题的时空谱方法。半离散方法在 L 2 {L^{2}} 规范下获得了最佳收敛阶数。 -norm。该方法的离散方案在空间方向上基于改进的傅立叶伪谱法，在时间方向上基于 Legendre-tau 法。非线性项通过快速傅立叶变换和快速 Legendre 变换计算。该方法通过显式-隐式迭代法实现。给出的数值结果表明了这种时空谱方法的准确性和能力。

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Determination of an unknown coefficient in the Korteweg–de Vries equation

In this paper, a space-time spectral method for solving an inverse problem in the Korteweg–de Vries equation is considered. Optimal order of convergence of the semi-discrete method is obtained in L 2

{L^{2}}

-norm. The discrete schemes of the method are based on the modified Fourier pseudospectral method in spatial direction and the Legendre-tau method in temporal direction. The nonlinear term is computed via the fast Fourier transform and fast Legendre transform. The method is implemented by the explicit-implicit iterative method. Numerical results are given to show the accuracy and capability of this space-time spectral method.

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来源期刊

Journal of Inverse and Ill-Posed Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published. Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest. The following topics are covered: Inverse problems existence and uniqueness theorems stability estimates optimization and identification problems numerical methods Ill-posed problems regularization theory operator equations integral geometry Applications inverse problems in geophysics, electrodynamics and acoustics inverse problems in ecology inverse and ill-posed problems in medicine mathematical problems of tomography