| 解带有扰动数据的第一类Volterra积分方程的谱正则化方法 |
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| 引用本文： | 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(A辑), 2020, 0(3): 650-661 |
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| 作者姓名： | 冯立新 杨晓旭 |
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| 作者单位： | 黑龙江大学数学科学学院;黑龙江省复杂系统理论与计算重点实验室 |
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| 基金项目： | 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)。 |
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| 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.
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| 关 键 词： | 谱方法 正则化策略 Volterra积分方程 收敛分析 |
Spectral Regularization Method for Volterra Integral Equation of the First Kind with Noise Data |
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| Feng Lixin,Yang Xiaoxu. Spectral Regularization Method for Volterra Integral Equation of the First Kind with Noise Data[J]. Acta Mathematica Scientia, 2020, 0(3): 650-661 |
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| Authors: | Feng Lixin Yang Xiaoxu |
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| Affiliation: | (Department of Mathematics,Heilongjiang University,Harbin 150080;Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems,Harbin 150080) |
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| 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. |
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| Keywords: | Spectral method Regularization strategy Volterra integral equation Convergence analysis |
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