| 非线性比例尺微分方程组的稳定性分析及数值处理 |
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| 引用本文： | 单恺婷,江峰,匡蛟勋,田红炯. 非线性比例尺微分方程组的稳定性分析及数值处理[J]. 上海师范大学学报(自然科学版), 2009, 38(2) |
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| 作者姓名： | 单恺婷 江峰 匡蛟勋 田红炯 |
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| 作者单位： | 上海师范大学,数理学院,上海,200234 |
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| 摘 要： | 主要研究了多延时非线性比例尺方程理论解及数值解的稳定性质Y'(t)=f(t,y(t),y( λd t)t…,y(λd t)),其中f:R×CN×…×CN→CN,y:R→CN,0< λd<…< λ1<1.获得了比例尺微分方程稳定及渐近稳定的充分条件, 同时研究了隐式欧拉方法的稳定性质.
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| 关 键 词： | 比例尺微分方程 稳定性 时滞微分方程 |
Analysis and numerical treatment for nonlinear systems of pantograph equations with many delays |
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| SHAN Kai-ting,JIANG Feng,KUANG Jiao-xun,TIAN Hong-jiong. Analysis and numerical treatment for nonlinear systems of pantograph equations with many delays[J]. Journal of Shanghai Normal University(Natural Sciences), 2009, 38(2) |
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| Authors: | SHAN Kai-ting JIANG Feng KUANG Jiao-xun TIAN Hong-jiong |
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| Affiliation: | Mathematics and Science College;Shanghai Normal University;Shanghai 200234;China |
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| Abstract: | This paper deals with the stability properties of the analytic and numerical solutions of nonlinear systems of pantograph differential equations with many delays.Sufficient conditions for the trivial solutions of the pantograph differential equations to be stable and asymptotically stable are derived.We also focus on the corresponding numerical stability properties of the implicit Euler method solving the underlying differential equation. |
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| Keywords: | pantograph differential equation stability delay differential equation |
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