一類常微分方程多點(diǎn)自由邊值問題的數(shù)值計(jì)算

信息計(jì)算科學(xué)論文編號:XXLW080 論文字?jǐn)?shù):7354,頁數(shù):44

 目錄
中文摘要 i
英文摘要………………………………………………………………………………………… ii
目錄………………………………………………………………………………………………iii
第一章    背景…………………………………………………………………………………  1
第二章    常微分方程自由邊值問題…………………………………………………………  3
       2.1  模型的提出………………………………………………………  3
       2.2  解得定性分析…………………………………………………  4
第三章    具體算法………………………………………………………   8
 第四章    結(jié)論…………………………………………………………… 11
致謝……………………………………………………… 12
參考文獻(xiàn)……………………………………………………………… 13
附錄……………………………………………………… 14

摘     要
    本文首先提出了金融數(shù)學(xué)在金融市場和資本市場中的重要性，而且在眾多的控制策略中經(jīng)典的脈沖控制策略對金融問題進(jìn)行最優(yōu)控制尤為重要。通常這種最優(yōu)控制策略的存在性和最優(yōu)控制策略的構(gòu)造歸結(jié)為常微分方程。本文對該問題的常微分方程的解存在性及具體的數(shù)值方法進(jìn)行了討論。在求解的過程中，從一定的約束條件，提出了解存在需滿足的三個(gè)定理,給出了一種簡單可行的求解方法。由于我們的方法是構(gòu)造性的，通過程序給出一組參數(shù)的數(shù)值解。
關(guān)鍵詞：脈沖控制策略  常微分方程  數(shù)值方法

Abstract
 First, the paper has raised the importance of financial mathematics in the financial and capital markets, and the classical impulse control strategy of the many control strategy on financial issues for optimal control is particularly important. Usually the existence and the structure of    optimal control strategy come down to the ordinary differential equations. The paper has discussed the issue in the existence of ordinary differential equations solutions and the specific numerical methods. In this solution process, we are raising three theorems that the solution should meet and giving a simple and feasible solution form constrain conditions. Because our analytical method is constructive, so we give a group parameters of numerical solution by procedure.
 Keywords： Impulse control strategy; Ordinary differential equations; Numerical methods