In this paper, a split-step theta algorithm is proposed for nonlinear stochastic variable delay differential equations. It is proved that the numerical solution obtained by the algorithm converges to the exact solution under the local Lipschitz condition. Moreover, it is shown that the numerical algorithm can maintain the mean square stability of the analytical solution for linear scalar equations. Finally, numerical experiments demonstrate the correctness of the theoretical algorithm.
机构:
Semnan Univ, Fac Math Stat & Comp Sci, Dept Math, POB 35195-363, Semnan, IranSemnan Univ, Fac Math Stat & Comp Sci, Dept Math, POB 35195-363, Semnan, Iran