中山大学学报自然科学版 ›› 2018, Vol. 57 ›› Issue (1): 55-62.

• 论文 • 上一篇    下一篇

带非线性延迟项的分数阶微分积分方程收敛性

郑伟珊   

  1. 韩山师范学院数学与统计学院,广东 潮州 521041
  • 收稿日期:2017-05-16 出版日期:2018-01-25 发布日期:2018-01-25
  • 通讯作者: 郑伟珊(1983年生),女;研究方向:计算数学

Convergence analysis for fractional integral and differential equation with nonlinear delay

ZHENG Weishan   

  1. Colloge of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China
  • Received:2017-05-16 Online:2018-01-25 Published:2018-01-25

摘要:

采用Jacobi谱配置方法研究带非线性延迟项的分数阶微分积分方程,通过适当的线性变换后利用雅可比高斯求积公式求近似解和近似导数,并给出严格的误差分析,证明了在无穷范数和加权L2加权范数中精确解与近似解,精确导数与近似导数的误差均呈指数衰减。

关键词: Jacobi谱配置方法, 非线性延迟项, 分数阶导数, 微分积分方程, 高斯求积公式, 收敛分析

Abstract:

The fractional integral and differential equation with nonlinear delay is studied with Jacobi spectralcollocation method. After proper linear transformation, an approximate solution and an approximate derivative of the solution are obtained by Gauss quadrature formula. By Jacobi collocation discretization, a rigorous error analysis is provided to show that the error of the approximate solution and the error of the approximate derivative both decay exponentially in the infinity norm and the weighted L2-norm.

Key words: Jacobi spectral-collocation method, nonlinear delay, fractional derivative, the fractional integral and differential equation, Gauss quadrature formula, convergence analysis

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