广东工业大学学报 ›› 2022, Vol. 39 ›› Issue (02): 62-65.doi: 10.12052/gdutxb.200125

• 综合研究 • 上一篇    下一篇

分数阶捕食者—食饵模型的变分迭代法

岑达康, 汪志波   

  1. 广东工业大学 数学与统计学院, 广东 广州 510520
  • 收稿日期:2020-09-22 出版日期:2022-03-10 发布日期:2022-04-02
  • 通信作者: 汪志波(1987-)，男，副教授，主要研究方向为微分方程数值解，E-mail：wzbmath@gdut.edu.cn
  • 作者简介:岑达康(1997-)，男，硕士研究生，主要研究方向为微分方程数值解
  • 基金资助:
    国家自然科学基金资助项目(11701103)；广东省珠江人才计划引进高层次人才项目(2017GC010379)；广东省自然科学基金资助项目(2019A1515010876)；广东省计算科学重点实验室开放基金(2021023)；广州市科技计划一般项目(201904010341，202102020704)

A Variational Iteration Method for Fractional Predator-Prey Model

Cen Da-kang, Wang Zhi-bo   

  1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2020-09-22 Online:2022-03-10 Published:2022-04-02

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摘要： 讨论了一类分数阶捕食者—食饵模型的变分迭代方法(Variational Iteration Method,VIM)。对该模型进行积分变换，得到与之等价的耦合积分微分方程组。根据变分原理，得出拉格朗日乘子，构建VIM求解格式，并对求解格式的收敛性进行分析。最后进行了相关的数值模拟，模拟结果验证了该方法的可行性和有效性。

关键词: 分数阶捕食者?食饵模型, 变分迭代方法, 收敛性

Abstract: A variational iteration method (VIM) for a class of fractional predator-prey model is studied. A pair equivalent coupled integro-differential equation to the model is obtained by means of integral transformation. According to variational theory, the Lagrange multiplier is calculated and the VIM scheme is constructed. Finally, a convergence analysis of the scheme is given and a numerical simulation is carried out.The results verify the feasibility and effectiveness of the method.

Key words: fractional predator-prey model, variational iteration method, convergence

中图分类号: 

  • O241.8
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[1] 张会琴, 汪志波. 带周期边界的时间分数阶扩散方程的差分格式[J]. 广东工业大学学报, 2019, 36(03): 74-79.
[2] 莫浩艺； . 解一类广义线性互补问题的神经网络模型[J]. 广东工业大学学报, 2007, 24(2): 20-23.
[3] 惠阿丽； 郑建明； 孙瑜； . 非线性系统闭环PD型迭代学习收敛性分析[J]. 广东工业大学学报, 2006, 23(2): 42-47.
[4] 肖胜中； 古伟清； . 求解带不可微项方程的Newton-Moser迭代的收敛性[J]. 广东工业大学学报, 2000, 17(1): 88-91.
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