延迟微分方的再生核数值解法.pdf

国内图书分类号:
国际图书分类号:51
理学硕士学位论文
延迟微分方程的再生核数值解法
研究生: 杜萍
导师: 金承日教授
申请学位: 理学硕士
学科、专业: 计算数学
所在单位: 数学系
答辩日期: 2006 年 6 月
授予学位单位: 哈尔滨工业大学
Classified Index:
: 51
Thesis for the Master Degree in Science
THE NUMERICAL SOLUTION OF DELAY
DIFFERENTIAL EQUATIONS VIA
REPRODUCING KERNEL THEORY
Candidate: ping du
Supervisor: Prof. chengri jin
Academic Degree Applied for: Master of Science
Specialty: Computational Mathematics
Affilication: Department of Mathematics
Date of Defence: June, 2006
Degree-Conferring-Institution: Harbin Institute of Technology
哈尔滨工业大学硕士学位论文
摘摘摘要要要
延迟问题也称为时滞问题,它在各个学科领域都有很重要的应用,也是
目前各学科普遍面临的重要研究对象。延迟微分方程就是指带有延迟项的微
分方程,求解这类方程的方法有很多, 本文主要是研究用再生核理论求解延
迟微分方程的数值方法。
本文在前人工作的基础上应用再生核的理论给出了中立型线性延迟微分
方程的数值解法。此外, 也给出了非线性的比例延迟微分方程的数值解法。
在第一章中介绍了延迟微分方程的发展史和再生核理论的历史。对延迟
微分方程有了初步的了解, 随后介绍了 W [a, b] 空间中有关再生核的性质和理
论, 并在这些理论的基础上以线性中立型延迟微分方程和非线性比例延迟微
分方程为模型, 探讨了他们的再生核数值解法。
关键词再生核;中立型延迟微分方程;非线性比例延迟微分方程;精确
解;数值解
– I –
哈尔滨工业大学硕士学位论文
Abstract
In this thesis,the main problem is how to solve linear and nonlinear delay equa-
tions by use of the theory of reproducing first chapter discussed the gen-
eral developing progress of delay equations and reproducing second chap-
ter give the main characterization about reproducing this chapter,we
know the base theory of the reproducing the third chapter we use the repro-
ducing kernel theory to solve linear neutral delay differential equations,from which
we know the exact solution and numerical solution ,and the error is well. We con-
clude that the possibility of this method, In the last chapter we use this theory to solve
nonlinear pantograph delay equations and the result is also we have known
much about reproducing kernel,There are still many fields we should to study about
it.
Key Words Reproducing kernel,Neutral delay differential equations,nonlinear
pantograph equations,exact solution,Nume