随机常微分方程的保正格式
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随机微分方程(SDEs)是生物学、物理学、经济学等领域的重要数学模型.在实际应用中，大量随机微分方程具有非线性且其精确解为正值的特征.由于其精确解通常无显式表达式，研究随机微分方程的保正数值格式对以上领域的发展具有重要的意义.本学位论文提出了几类求解随机常微分方程的新保正数值格式，并探讨其稳定性和收敛性.新格式通过引入Lagrange乘子和Karush-Kuhn-Tucker(KKT)条件，利用预测-校正法，使得数值格式保正.全文共分为六章. 第一章概述本文研究内容的相关背景及国内外的研究现状，介绍沈捷教授[50]最新关于确定型偏微分方程的保正数值格式，然后阐述本文的主要结果，最后给出本文用...
Stochastic differential equations (SDEs) are important mathematical models in the fields of biology, physics and economics etc. In practical applications, a majority of stochastic differential equations are nonlinear and own positive solutions. Since exact solution of most of stochastic differential equations does not have explicit expressions, it is very important to develop positivity preserving...
Stochastic differential equations (SDEs) are important mathematical models in the fields of biology, physics and economics etc. In practical applications, a majority of stochastic differential equations are nonlinear and own positive solutions. Since exact solution of most of stochastic differential equations does not have explicit expressions, it is very important to develop positivity preserving...