An efficient drift-tamed approximation to the stochastic parabolic integro-differential equation with Allen-Cahn potential

This paper develops an efficient fully discrete scheme for approximating the stochastic semilinear parabolic integro-differential equation with Allen-Cahn nonlinear term, based on a drift-tamed time discretization combined with a finite element spatial approximation. The proposed full discretization method is shown to be unconditionally stable and computationally efficient. Furthermore, the spatio-temporal strong convergence rate of the proposed scheme is rigorously established in spatial dimensions d ∈ {1, 2, 3} by exploiting the stability estimates of the numerical solution. Numerical experiments are reported to validate the theoretical results and to demonstrate the improved robustness of the proposed method compared with the untamed scheme.

Citation

Qi, X., Li, H., Sun, Y., & Yan, Y. (2026). An efficient drift-tamed approximation to the stochastic parabolic integro-differential equation with Allen-Cahn potential. Communications in Nonlinear Science and Numerical Simulation, 163(1), 110468. https://doi.org/10.1016/j.cnsns.2026.110468

Publisher

Elsevier

Journal

Communications in Nonlinear Science and Numerical Simulation

URI

https://chesterrep.openrepository.com/handle/10034/630054

DOI

10.1016/j.cnsns.2026.110468

Type

Article

Description

ISSN

1007-5704

EISSN

1878-7274

Additional Links

https://www.sciencedirect.com/science/article/pii/S1007570426008221?via%3Dihub