@Article{JMS-56-4,
author = {Xiao, Qi},
title = {Extended Milstein Approximation to the Stochastic Allen-Cahn Equation with Random Diffusion Coefficient Field and Multiplicative Noise},
journal = {Journal of Mathematical Study},
year = {2023},
volume = {56},
number = {4},
pages = {366--391},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v56n4.23.05},
url = {https://global-sci.com/article/87632/extended-milstein-approximation-to-the-stochastic-allen-cahn-equation-with-random-diffusion-coefficient-field-and-multiplicative-noise}
}