天津师范大学学报（自然科学版）2025，Vol.45Issue(2)：1-8,8.DOI:10.19638/j.issn1671-1114.20250201
比例时滞奇异微分方程的级数解与Chebyshev配置法
Series solution and Chebyshev collocation method for singular differential equation with a proportional delay
摘要
Abstract
The numerical solution of singular differential equation with a proportional delay is studied.Firstly,the series expansion for the solution about the origin is derived by Picard iteration for the equation.And then,considering the series solu-tion,an accurately smoothing transformation is designed to make the solution of the equation smooth enough.For the trans-formed equation,the Chebyshev-Gauss-Radau collocation methods in differential and integral forms are designed to obtain the numerical solution of the equation on a finite interval.It is proved that the method in integral form has optimal convergence with respect to maximum norm.Numerical examples demonstrate the high accuracy of the proposed methods in solving delay differ-ential equations.关键词
比例时滞奇异微分方程/分数阶级数解/光滑变换/Chebyshev-Gauss-Radau配置法Key words
singular differential equation with a proportional delay/fractional series solution/smoothing transformation/Chebyshev-Gauss-Radau collocation method分类
数学引用本文复制引用
陈宏,王同科..比例时滞奇异微分方程的级数解与Chebyshev配置法[J].天津师范大学学报（自然科学版）,2025,45(2):1-8,8.基金项目
国家自然科学基金资助项目(11971241) （11971241）
天津师范大学研究生科研创新资助项目(2024KYCX108Y). （2024KYCX108Y）
