随机时滞微分方程的截断Caratheodory数值解的收敛性

Convergence of the Truncated Caratheodory Numerical Solution for a Stochastic Delay Differential Equation

将截断方法引入非线性随机时滞微分方程的数值解构造中,构建了截断Caratheodory数值算法,当系数满足局部Lipschitz条件和Khasminskii型条件时,存在唯一的解析解。同样的条件下,在证明数值解的有界性基础上,通过分析数值解的误差验证了数值解的收敛性,并且给出了数值解的收敛阶数。

By introducing the truncated method into a nonlinear stochastic delay differential equation,a truncated Caratheodory numerical algorithm is constructed.As coefficients satisfy the local Lipschitz condition and the Khasminskii type condition,the unique explicit solution for the equation exists.Under the same conditions,based on the boundedness of the solution,the convergence of the numerical solution is proved through analyzing the error of numerical and explicit solutions.The convergence order of the numerical solution is also given.