Poisson跳的随机延迟微分方程Heun方法的均方收敛性  

Mean-square Convergence of Heun Method for Stochastic Delay Differential Equation with Poisson Jumps

作　　者：易玉连 王文强[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《应用数学》2015年第4期938-948,共11页Mathematica Applicata

基　　金：国家自然科学基金(11271311;11171352);湖南省教育厅重点项目(14A146)

摘　　要：Heun方法是一类求解随机延迟微分方程的数值方法,本文试图研究Poisson跳的随机延迟微分方程Heun方法的均方收敛性.当Poisson跳的随机延迟微分方程满足一定约束条件时,获得Heun方法求解方程所得的数值解收敛于真解,且均方收敛阶为1的理论结果2.文末数值试验的结果验证了理论结果的正确性.Heun method is a significant numerical method for solving stochastic delay differential equations, and this paper deals with the convergence of Heun method for stochastic delay differential equations with Poisson jumps. It is proved that the numerical solutions of Heun method converge to the 1/2 when the stochastic delay differential equations with Poisson jumps true solution in mean square order ~ , satisfy certain constraints. Results of Numerical experiments in the end verify the theoretical results.

关 键 词：随机延迟微分方程 Heun方法 POISSON跳 均方收敛 

分 类 号：O241.81[理学—计算数学]