摘要
随着时代的发展,自变量分段连续型微分方程(SEPCAs)越来越多地获得了人们的广泛关注,并且能够成功地将其应用到工学、理学、医学、生物学等诸多领域.为了探索SEPCAs对欧拉方法的强收敛性.利用微分方程求解的方式分别证明了在局部Lipschitz条件和p阶矩有界条件下、在局部Lipschitz条件和线性增长条件下、在局部Lipschitz条件(H_(1))和单调条件(H_(3))下Euler-Maruyama法对SEPCAs方程具有强收敛性,并通过算例分析证明了Euler-Maruyama法在不同步长下数值解的收敛情况.
With the development of the times,independent variable piecewise continuous differential equations(sepcas)have attracted more and more attention,and can be successfully applied to many fields such as engineering,science,medicine,biology and so on.In order to explore the strong convergence of sepcas to Euler method.By solving differential equations,it is proved that the Euler Maruyama method has strong convergence for sepcas equations under local Lipschitz condition and bounded p-order moment condition,local Lipschitz condition and linear growth condition,local Lipschitz condition(H_(1))and monotone condition(H_(3)).The convergence of the numerical solution of Euler Maruyama method under asynchronous length is proved by numerical example analysis.
作者
宋丽雅
Song Liya(Changzhi Preschool Education College)
出处
《哈尔滨师范大学自然科学学报》
CAS
2022年第1期36-43,共8页
Natural Science Journal of Harbin Normal University
关键词
分段连续型随机微分方程
指数欧拉方法
强收敛
数值解
Piecewise continuous stochastic differential equation
Exponential Euler method
Strong convergence
Numerical solution
