随机变延迟微分方程平衡方法的收敛性和稳定性

Convergence and Stability of Balanced Methods for Stochastic Variable Delay Differential Equations

利用全隐式数值方法平衡方法讨论一类随机变延迟微分方程的收敛性和稳定性.首先,证明该方程数值解以1/2阶均方收敛到精确解;其次,证明该方法能保持解析解的均方稳定性;最后,通过数值实验验证理论结果的正确性.

We discussed the convergence and stability by using the fully implicit numerical method—balanced methods for a class of stochastic variable delay differential equations.Firstly,we proved that the numerical solution of the equation converged to the exact solution in 1/2 order mean-square.Secondly,we proved that the method could keep the mean-square stability of the analytical solution.Finally,the correctness of the theoretical results was verified by numerical experiments.