TY - JOUR
T1 - A Truncated-Type Explicit Numerical Method for the Stochastic Allen-Cahn Equation
AU - Zhan , Weijun
AU - Guo , Qian
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 295
EP - 314
PY - 2024
DA - 2024/12
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2022-0240
UR - https://global-sci.org/intro/article_detail/aamm/23603.html
KW - Stochastic Allen-Cahn equations, truncated Euler–Maruyama, spectral Galerkin method, strong convergence.
AB - <p style="text-align: justify;">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.</p>