A Truncated-Type Explicit Numerical Method for the Stochastic Allen-Cahn Equation (Advances in Applied Mathematics and Mechanics, 2024)
The stochastic Allen-Cahn equations, as a typical example of nonlinearstochastic partial differential equations, play an important role in phase theory. Inthis paper, we investigate the rate of convergence in the $p{\rm th}$ mean for a truncated-typeexplicit Euler time-stepping method applied to the stochastic Allen-Cahn equations aswell as using the spectral Galerkin approximation in spatial discretization. Finally, anumerical example is given to confirm the strong convergence order.