科研成果详情

发表状态已发表Published
题名On spectral methods for Volterra integral equations and the convergence analysis
作者
发表日期2008
发表期刊Journal of Computational Mathematics
ISSN/eISSN0254-9409
卷号26期号:6页码:825-837
摘要

The main purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on a spectral approach. A Legendre-collocation method is proposed to solve the Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors decay exponentially provided that the kernel function and the source function are sufficiently smooth. Numerical results confirm the theoretical prediction of the exponential rate of convergence. The result in this work seems to be the first successful spectral approach (with theoretical justification) for the Volterra type equations.

关键词Convergence analysis Legendre-spectral method Second kind Volterra integral equations
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收录类别SCIE
语种英语English
WOS研究方向Mathematics
WOS类目Mathematics, Applied ; Mathematics
WOS记录号WOS:000261217600004
Scopus入藏号2-s2.0-57149087968
引用统计
被引频次:219[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符https://repository.uic.edu.cn/handle/39GCC9TT/1820
专题个人在本单位外知识产出
通讯作者Tang, Tao
作者单位
1.Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
2.School of Mathematics, Fudan University, Shanghai 200433, China
推荐引用方式
GB/T 7714
Tang, Tao,Xu, Xiang,Cheng, Jin. On spectral methods for Volterra integral equations and the convergence analysis[J]. Journal of Computational Mathematics, 2008, 26(6): 825-837.
APA Tang, Tao, Xu, Xiang, & Cheng, Jin. (2008). On spectral methods for Volterra integral equations and the convergence analysis. Journal of Computational Mathematics, 26(6), 825-837.
MLA Tang, Tao,et al."On spectral methods for Volterra integral equations and the convergence analysis". Journal of Computational Mathematics 26.6(2008): 825-837.
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