Banach空间中非线性中立型泛函微分方程θ-方法的收缩性

Nonlinear Contractivity of θ-methods for Neutral Functional Differential Equations in Banach Space

中立型泛函微分方程(NFDEs)广泛出现于生物学、物理学、控制理论以及工程技术等领域,近四十年来人们对其进行了大量研究。但由于其困难性,对其数值解的研究基本局限于线性问题和一些特殊的非线性问题,而对于更为一般的中立型非线性初值问题的研究很少。这篇文章致力于研究巴拿赫空间中非线性中立型泛函微分方程初值问题θ-方法的非线性收缩性,获得了θ-方法求解NFDEs的收缩性的结果 。

Neutral functional differential equations （NFDEs） can be found in many scientific and technological fields such as biology, physics, control theory, engineering an so on. In the last four decades, it have been widely discussed by many authors. But because of the difficulty of the research, its numerical solutions is still limited to linear problems and several classes of special nonlinear problems so far. For more general nonlinear NFDEs, there have little research in literature. This paper is concerned with the numerical solution to initial value problems of nonlinear neutral functional differential equations in Banach space. Contractivity results of θ-methods is obtained.