Extended Milstein Approximation to the Stochastic Allen-Cahn Equation with Random Diffusion Coefficient Field and Multiplicative Noise
Year: 2023
Author: Xiao Qi
Journal of Mathematical Study, Vol. 56 (2023), Iss. 4 : pp. 366–391
Abstract
This paper studies the stochastic Allen-Cahn equation driven by a random diffusion coefficient field and multiplicative force noise. A new time-stepping scheme based on a stabilized approach and Milstein scheme is proposed and analyzed. The proposed method is unconditionally stable in the sense that a discrete energy is dissipative when the multiplicative noise is absent. The strong convergence rate of a spatio-temporal fully discrete scheme is derived. Numerical experiments are finally reported to confirm the theoretical result and show that the new scheme is much more robust than the classical semi-implicit Euler-Maruyama scheme, especially when the interface width parameter is small.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v56n4.23.05
Journal of Mathematical Study, Vol. 56 (2023), Iss. 4 : pp. 366–391
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Stochastic Allen-Cahn equation multiplicative noise strong convergence extended Milstein scheme stability.