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Volume 17, Issue 1
A Truncated-Type Explicit Numerical Method for the Stochastic Allen-Cahn Equation

Weijun Zhan & Qian Guo

Adv. Appl. Math. Mech., 17 (2025), pp. 295-314.

Published online: 2024-12

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  • 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.

  • AMS Subject Headings

60H35, 60H15

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COPYRIGHT: © Global Science Press

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@Article{AAMM-17-295, author = {Zhan , Weijun and Guo , Qian}, title = {A Truncated-Type Explicit Numerical Method for the Stochastic Allen-Cahn Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2024}, volume = {17}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0240}, url = {http://global-sci.org/intro/article_detail/aamm/23603.html} }
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 -

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.

Zhan , Weijun and Guo , Qian. (2024). A Truncated-Type Explicit Numerical Method for the Stochastic Allen-Cahn Equation. Advances in Applied Mathematics and Mechanics. 17 (1). 295-314. doi:10.4208/aamm.OA-2022-0240
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