本文選題：穩(wěn)定 + 非線性滯時(shí)微分代數(shù)方程　； 參考：《上海師范大學(xué)》2015年碩士論文

【摘要】：滯時(shí)微分代數(shù)方程(DDAEs)是具有時(shí)滯影響和代數(shù)約束的微分方程,為計(jì)算機(jī)輔助設(shè)計(jì)、化學(xué)反應(yīng)模擬、線路分析、最優(yōu)控制、實(shí)時(shí)仿真以及管理系統(tǒng)等科學(xué)與工程應(yīng)用問題提供了有效的數(shù)學(xué)模型.目前,關(guān)于線性滯時(shí)微分代數(shù)方程的穩(wěn)定性與數(shù)值算法的研究較多,但對于非線性滯時(shí)微分代數(shù)方程的研究很少,本文主要研究一類非線性滯時(shí)微分代數(shù)方程及其數(shù)值算法的穩(wěn)定性與漸近穩(wěn)定性.首先,根據(jù)穩(wěn)定與漸近穩(wěn)定的定義,我們給出了方程穩(wěn)定和漸近穩(wěn)定的充分條件,其次,討論了用2階BDF算法求解這類滯時(shí)微分代數(shù)方程所得數(shù)值解的穩(wěn)定性與漸近穩(wěn)定性,最后,給出了一些數(shù)值實(shí)驗(yàn)來驗(yàn)證本文理論的正確性.
[Abstract]:Delay differential algebraic equation (DDAEs) is a differential equation with time-delay effect and algebraic constraint. It is used for computer-aided design, chemical reaction simulation, circuit analysis, optimal control, etc. Real-time simulation and management systems provide an effective mathematical model for scientific and engineering applications. At present, there are many researches on the stability and numerical algorithms of linear delay differential algebraic equations, but few on nonlinear delay differential algebraic equations. In this paper, the stability and asymptotic stability of a class of nonlinear delay differential algebraic equations and their numerical algorithms are studied. Firstly, according to the definitions of stability and asymptotic stability, we give the sufficient conditions for the stability and asymptotic stability of the equations. Secondly, we discuss the stability and asymptotic stability of the numerical solutions obtained by using the second-order BDF algorithm to solve this kind of delay differential algebraic equations. Finally, some numerical experiments are given to verify the correctness of the theory.
【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O241.8

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本文編號：1953070