Convergence and stability of split-step θ methods for stochastic variable delay differential equations

Abstract

In this paper, a split-step θ 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.

Keywords:

• Stochastic variable delay differential equations
• split-step θ method
• local Lipschitz condition
• strong convergence
• mean square stability

2010 MSC Classifications:

• 65L05
• 60C20

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This study was funded by : National Natural Science Foundation of China [grant numbers 11801238,11561028].