Year: 2025
Author: Weijun Zhan, Qian Guo
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 295–314
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0240
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 295–314
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Stochastic Allen-Cahn equations truncated Euler–Maruyama spectral Galerkin method strong convergence.