Abstract
The main aim of this work is to prove that the backward Euler–Maruyama approximate solutions converge strongly to the true solutions for stochastic functional differential equations with superlinear growth coefficients. The paper also gives the boundedness and mean-square exponential stability of the exact solutions, and shows that the backward Euler–Maruyama method can preserve the boundedness of mean-square moments. Finally, a highly nonlinear example is provided to illustrate the main results.
| Original language | English |
|---|---|
| Pages (from-to) | 241-257 |
| Number of pages | 17 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 324 |
| DOIs | |
| Publication status | Published - 1 Nov 2017 |
Keywords
- Backward Euler–Maruyama method
- Boundedness
- Polynomial growth condition
- Stochastic functional differential equation
- Strong convergence
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Zhou, S., & Jin, H. (2017). Strong convergence of implicit numerical methods for nonlinear stochastic functional differential equations. Journal of Computational and Applied Mathematics, 324, 241-257. https://doi.org/10.1016/j.cam.2017.04.015