摘要
研究了一阶时滞非线性微分方程的近似解析解.以直接展开法为主要研究工具,首先运用直接展开法构造原问题的近似解表达式,再应用不动点定理给出原问题解的存在性的证明,最后借助数学软件MATLAB进行数值模拟,对其精确解及近似解进行对比,验证所得结果.
A class of approximate analytic solution of nonlinear differential equation with time-delay was studied.By using direct expansion method,the approximate solution expression of the original problem was constructed.Then the fixed point theorem was applied to prove the existence of solutions to the original problem.Finally,mathematical software MATLAB was employed for numerical simulation and comparison of the exact solution with the approximate solution to this problem,and the results were verified as well.
出处
《上海应用技术学院学报（自然科学版）》
2014年第4期353-357,共5页
Journal of Shanghai Institute of Technology: Natural Science
基金
上海应用技术学院引进人才基金资助项目(YJ2013-33)
关键词
时滞
非线性微分方程
直接展开法
近似解析解
MATLAB
time-delay
nonlinear differential equation
direct expansion method
approximate analytic solution
MATLAB
