Adv. Appl. Math. Mech., 17 (2025), pp. 295-314.
Published online: 2024-12
Cited by
- BibTex
- RIS
- TXT
The stochastic Allen-Cahn equations, as a typical example of nonlinear stochastic partial differential equations, play an important role in phase theory. In this paper, we investigate the rate of convergence in the $p{\rm th}$ mean for a truncated-type explicit Euler time-stepping method applied to the stochastic Allen-Cahn equations as well as using the spectral Galerkin approximation in spatial discretization. Finally, a numerical example is given to confirm the strong convergence order.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0240}, url = {http://global-sci.org/intro/article_detail/aamm/23603.html} }The stochastic Allen-Cahn equations, as a typical example of nonlinear stochastic partial differential equations, play an important role in phase theory. In this paper, we investigate the rate of convergence in the $p{\rm th}$ mean for a truncated-type explicit Euler time-stepping method applied to the stochastic Allen-Cahn equations as well as using the spectral Galerkin approximation in spatial discretization. Finally, a numerical example is given to confirm the strong convergence order.