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

被引：0

作者：

Sang, Lin ^{[1
,2
]}

Qiao, Yan ^{[1
,2
]}

Wu, Hua ^{[1
,2
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

[2] Shanghai Univ, Newtouch Ctr Math, Shanghai 200444, Peoples R China

来源：

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS | 2024年 / 32卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Korteweg-de Vries equation; inverse problem; error estimate; spectral method; CHEBYSHEV COLLOCATION METHOD; PARABOLIC INVERSE PROBLEM; GALERKIN;

D O I：

10.1515/jiip-2024-0008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1277 / 1289

页数：13

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