| 基于Chebyshev神经网络的非线性Fredholm积分方程数值解法 |
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| 引用本文： | 李娜,韩惠丽,房彦兵.基于Chebyshev神经网络的非线性Fredholm积分方程数值解法[J].吉林大学学报(理学版),2020,58(2):277-284. |
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| 作者姓名： | 李娜 韩惠丽 房彦兵 |
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| 作者单位： | 宁夏大学 数学统计学院, 银川 750021 |
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| 基金项目： | 宁夏高等学校自然科学研究项目;宁夏自然科学基金 |
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| 摘 要： | 利用Chebyshev扩展块代替隐层结构, 提出一种基于函数逼近的Chebyshev神经网络模型求解非线性Fredholm积分方程的方法, 并给出其最佳逼近解及算法的收敛性分析. 数值算例验证了算法的可行性和有效性.
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| 关 键 词： | Chebyshev多项式 神经网络 Fredholm积分方程 |
| 收稿时间： | 2019-06-21 |
Numerical Algorithm of Nonlinear Fredholm IntegralEquation Based on Chebyshev Neural Network |
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| LI Na,HAN Huili,FANG Yanbing.Numerical Algorithm of Nonlinear Fredholm IntegralEquation Based on Chebyshev Neural Network[J].Journal of Jilin University: Sci Ed,2020,58(2):277-284. |
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| Authors: | LI Na HAN Huili FANG Yanbing |
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| Institution: | School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China |
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| Abstract: | Using the Chebyshev expansion block instead of the hidden layer structure, we proposed a method of Chebyshev neural network model based on function approximation to solve nonlinear Fredholm integral equations, and gave its best approximation solution and the convergence analysis of the algorithm. The feasibility and effectiveness of the algorithm were verified by numerical examples. |
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| Keywords: | Chebyshev polynomial neural network Fredholm integral equation |
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