隐式中立型Volterra泛函积分微分方程的数值方法研究

项目名称： 隐式中立型Volterra泛函积分微分方程的数值方法研究

项目编号： No.11201162

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 覃婷婷

作者单位： 华中科技大学

项目金额： 22万元

中文摘要： 时滞泛函微分方程是模拟自然和工程中受时滞因素影响的动力学系统的有力工具，其中含分布型时滞项的中立型泛函积分微分方程及其数值方法研究，是该领域的前沿开放性课题。本项目关注在热力学、材料学、黏弹性力学以及物理学等重要科学工程领域中具共性特征的隐式中立型Volterra泛函积分微分方程，由于中立项的隐式性以及包含了奇异系统，其理论分析和数值模拟都更为复杂，现有数值研究成果匮乏。鉴于此,本项目拟针对此类隐式中立型Volterra泛函积分微分方程，拓展现有常及偏泛函微分方程的优秀的数值方法，利用各种插值与迭代技巧，构制新型高效的数值算法，研究数值方法的收敛性、可解性、稳定性、耗散性等重要性质，并探索方法的高效实现技巧及在热传导、航空材料学、半导体装置等实际数学模型中的应用。本项目将填补该类方程的数值研究空白，丰富时滞泛函微分方程的数值方法及理论成果，为相关实际科学问题提供新的数值仿真算法和分析工具。

中文关键词： 泛函积分微分方程；中立型；数值方法；理论分析；

英文摘要： Functional differential Equations with delay arguments are powerful tools for the simulation of dynamical systems influenced by delay phenomenon arising in scientific and engineering fields. Among the rest, the neutral functional integral-differential equations with distributed delay items have been widely used in modelling delay dynamical systems, because they can reflect the actual time delay phenomenon much better. So far for the numerical analysis of neutral functional integral-differential equations, there are still a number of open problems. This project focuses on one of these open problems: the numerical treatment for implicit neutral Volterra functional integral-differential equations, which presented in the energetics,materials science, viscoelastic mechanics, physics, and other scientific and engineering problems. This kind of Volterra functional integral-differential equations have significant differences with the common neutral functional integral -differential equations. The neutral iterms are not explicit but implicit, and this kind of equations may contain singular systems, for which the theoretical analysis and numerical simulation are much more complicated, and the study of their numerical methods is still in its infancy. In view of this, our project is devoted to the numerical analysis for

英文关键词： Functional integro-differential equations；Neutral；Numerical methods；Theoretical analysis；