AMS-stability of the Euler-Maruyama method for linear neutral stochastic delay differential equations. (English) Zbl 1299.65012
Summary: Stability of the Euler-Maruyama method for linear neutral stochastic delay differential equations is considered. The definition of asymptotic mean square (AMS)-stability of numerical methods is established. The conditions of asymptotic mean square stability of the Euler-Maruyama method for the system are given. It is shown that the Euler-Maruyama method is AMS-stable under these conditions. The numerical examples are presented to support the obtained results.
MSC:
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 34K50 | Stochastic functional-differential equations |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 34K40 | Neutral functional-differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
