解带有扰动数据的第一类Volterra积分方程的谱正则化方法

数学物理学报 ›› 2020, Vol. 40 ›› Issue (3): 650-661.

解带有扰动数据的第一类Volterra积分方程的谱正则化方法

冯立新^1,^2,*(),杨晓旭²

¹ 黑龙江大学数学科学学院哈尔滨 150080
² 黑龙江省复杂系统理论与计算重点实验室哈尔滨 150080

收稿日期:2019-01-15 出版日期:2020-06-26 发布日期:2020-07-15
通讯作者: 冯立新 E-mail:fenglixin@hlju.edu.cn
基金资助:
国家自然科学基金(11871198);黑龙江省高校基础研究基金黑龙江大学专项基金项目(RCYJTD201804)

Spectral Regularization Method for Volterra Integral Equation of the First Kind with Noise Data

Lixin Feng^1,^2,*(),Xiaoxu Yang²

¹ Department of Mathematics, Heilongjiang University, Harbin 150080
² Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Harbin 150080

Received:2019-01-15 Online:2020-06-26 Published:2020-07-15
Contact: Lixin Feng E-mail:fenglixin@hlju.edu.cn
Supported by:
NSFC(11871198);the Fundamental Research Funds for the Universities of Heilongjiang Province Heilongjiang University Special Fund Project(RCYJTD201804)

摘要/Abstract

摘要：

该文的主要目的是通过使用Legendre配置方法和正则化策略来求解带有噪声数据的第一类Volterra积分方程，并给出该方法收敛性分析的严格数学证明.数值实验表明了该方法的有效性.

关键词: 谱方法, 正则化策略, Volterra积分方程, 收敛分析

Abstract:

The main purpose of this work is to solve the Volterra integral equation of the first kind with noise data by using both a Legendre-collocation method and a regularization strategy. We provide a rigorous convergence analysis for the proposed method. Some numerical tests are illustrated to demonstrate the validity and effectiveness of the proposed method.

Key words: Spectral method, Regularization strategy, Volterra integral equation, Convergence analysis

中图分类号:

O241.83

冯立新,杨晓旭. 解带有扰动数据的第一类Volterra积分方程的谱正则化方法[J]. 数学物理学报, 2020, 40(3): 650-661.

Lixin Feng,Xiaoxu Yang. Spectral Regularization Method for Volterra Integral Equation of the First Kind with Noise Data[J]. Acta mathematica scientia,Series A, 2020, 40(3): 650-661.

参考文献

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