解随机森林发展方程的半隐式欧拉法的收敛性

一般来说,大多数随机偏微分方程并不存在显式解,因此,数值方法是研究这类方程解的性质的十分有效的工具.应用半隐式欧拉方法求解一类随机森林发展方程,从而得到其近似解,并证明了当满足一些比线性增长条件和全局利普希茨条件弱的条件时,半隐式欧拉格式将依概率收敛于方程的解析解,其收敛阶为p=1/2.

Convergence of the semi - implicit Euler method for stochastic forest evolution equations

In order to approximate the solutions of a class of stochastic forest evolution equations, a numerical method will be given. In general, the explicit solutions of most of stochastic partial differential equations do not exist, so numerical methods are invaluable tools for us to explore their properties. This paper is to show that under some conditions which are weaker than linear growth condition and global Lip-schitz condition, the semi - implicit Euler scheme converges to the analytic solutions of the stochastic for-est evolution equations in probability. Then we get the order of convergence p=1/2.