  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. Error bounds in a strong sense are analyzed for both the
spatial semi-discretization and the spatio-temporal full discretization, with
convergence rates in both space and time explicitly identified. It turns out
that the obtained convergence rate of the new scheme is, in the temporal
direction, twice as high as existing ones in the literature. Numerical results
are finally reported to confirm the previous theoretical findings.
