An efficient explicit full-discrete scheme for strong approximation of stochastic Allen-Cahn equation

Understand

In Becker and Jentzen (2019) and Becker et al.

• (2017), an explicit temporal semi-discretization scheme and a space-time full-discretization scheme were, respectively, introduced and analyzed for the additive noise-driven stochastic Allen-Cahn type equations, with strong convergence rates recovered.
• The present work aims to propose a different explicit full-discrete scheme to numerically solve the stochastic Allen-Cahn equation with cubic nonlinearity, perturbed by additive space-time white noise.
• The approximation is easily implementable, performing the spatial discretization by a spectral Galerkin method and the temporal discretization by a kind of nonlinearity-tamed accelerated exponential integrator scheme.