基于GA-Chebyshev神经网络的分数阶Bagley-Torvik方程数值解法

doi:10.12286/jssx.j2021-0841

计算数学 ›› 2023, Vol. 45 ›› Issue (1): 109-129.DOI: 10.12286/jssx.j2021-0841

基于GA-Chebyshev神经网络的分数阶Bagley-Torvik方程数值解法

胡行华, 秦艳杰

辽宁工程技术大学优化与决策研究所, 阜新 123000

收稿日期:2021-07-15 出版日期:2023-02-14 发布日期:2023-02-13
基金资助:
教育部人文社会科学研究(21YJCZH204)项目,辽宁省自然科学基金(2020-MS-301)和辽宁省教育厅高等学校基本科研项目(LJ2020ZD002,LJ2019JL005,2022lslwtkt-069)资助.

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胡行华, 秦艳杰. 基于GA-Chebyshev神经网络的分数阶Bagley-Torvik方程数值解法[J]. 计算数学, 2023, 45(1): 109-129.

Hu Xinghua, Qin Yanjie. NUMERICAL SOLUTION OF FRACTIONAL BAGLEY-TORVIK EQUATIONS BASED ON GA-CHEBYSHEV NEURAL NETWORK[J]. Mathematica Numerica Sinica, 2023, 45(1): 109-129.

NUMERICAL SOLUTION OF FRACTIONAL BAGLEY-TORVIK EQUATIONS BASED ON GA-CHEBYSHEV NEURAL NETWORK

Hu Xinghua, Qin Yanjie

Institute of Optimization and Decision, Liaoning Technical University, Fuxin 123000, China

Received:2021-07-15 Online:2023-02-14 Published:2023-02-13
Supported by:
The project was supported by the National Key Research and Development Program of China (2019YFC1905301);National Natural Science Foundation of China (22078115,21776108,21690083,22008078).

本文基于现有的切比雪夫神经网络, 提出了一种利用遗传算法优化切比雪夫神经网络求解分数阶 Bagley-Torvik 方程数值解的新方法, 结合多点处的泰勒公式原理, 给出数值解的一般形式, 将原问题转化为求解无约束最小化问题. 与现有数值方法的数值结果进行比较表明了本文方法的可行性和有效性, 为分数阶微分方程中类似问题的求解提供了新的思路.

关键词： 切比雪夫神经网络, 遗传算法, 分数阶Bagley-Torvik方程, 数值解

In this article, based on the existing Chebyshev neural network, a new method using genetic algorithm to optimize the Chebyshev neural network to solve the numerical solution of fractional Bagley-Torvik equation is proposed. Combined with the Taylor’s formula principle at multiple points, the general form of numerical solution is given, and the original problem is transformed into an unconstrained minimization problem. The comparison with the numerical results of the existing numerical methods shows the feasibility and effectiveness of the proposed method, which provides a new idea for the solution of similar problems in fractional differential equations.

Key words: Chebyshev neural network, genetic algorithm, fractional Bagley-Torvik equations, numerial solution

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基于GA-Chebyshev神经网络的分数阶Bagley-Torvik方程数值解法

NUMERICAL SOLUTION OF FRACTIONAL BAGLEY-TORVIK EQUATIONS BASED ON GA-CHEBYSHEV NEURAL NETWORK

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