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A Truncated-Type Explicit Numerical Method for the Stochastic Allen-Cahn Equation

A Truncated-Type Explicit Numerical Method for the Stochastic Allen-Cahn Equation

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.

Author Details

Weijun Zhan

Qian Guo