| 一类具弱奇性核Volterra积分方程的配置法求解 |
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| 引用本文： | 张凯,张英楠,陈旭梅.一类具弱奇性核Volterra积分方程的配置法求解[J].吉林大学学报(理学版),2011,49(2):186-190. |
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| 作者姓名： | 张凯 张英楠 陈旭梅 |
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| 作者单位： | 1. 吉林大学 数学学院, 长春 130012,2. 江苏大学 理学院, 江苏 镇江 212013 |
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| 基金项目： | 国家自然科学基金，江苏大学高级专业人才科研启动基金 |
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| 摘 要： | 研究一类具弱奇性核Volterra积分方程的配置法求解. 利用压缩映射定理证明了该类方程解的存在唯一性, 构造了求解这类方程的配置算法, 并对算法进行误差分析, 数值实验结果验证了理论的正确性. 该数值方法可应用于更一般的非线性Volterra积分方程.
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| 关 键 词： | 弱奇性核 Volterra积分方程 配置法 |
| 收稿时间： | 2010-06-23 |
Collocation Method for Solving a Class of Volterra Integral Equations with Weakly Singular Kernel |
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| ZHANG Kai,ZHANG Ying-nan,CHEN Xu-mei.Collocation Method for Solving a Class of Volterra Integral Equations with Weakly Singular Kernel[J].Journal of Jilin University: Sci Ed,2011,49(2):186-190. |
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| Authors: | ZHANG Kai ZHANG Ying-nan CHEN Xu-mei |
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| Institution: | 1. College of Mathematics, Jilin University, Changchun 130012, China;2. Faculty of Science, Jiangsu University, Zhenjiang 212013, Jiangsu Province, China |
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| Abstract: | The authors proposed a collocation method for solving aclass of Volterra integral equations with weakly singular kernel. Firstly, we showed the existence and uniqueness of the solution by the contraction mapping theorem, and then constructed the collocation scheme for this kind of equations together with the error analysis. Finally, the numerical experiments verified our theoretical results. This numerical method is useful for general nonlinear Volterra integral equations. |
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| Keywords: | weakly singular kernel Volterra integral equation collocation method |
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