  We construct a positivity-preserving Lie--Trotter splitting scheme with
finite difference discretization in space for approximating the solutions to a
class of nonlinear stochastic heat equations with multiplicative space-time
white noise. We prove that this explicit numerical scheme converges in the
mean-square sense, with rate $1/4$ in time and rate $1/2$ in space, under
appropriate CFL conditions. Numerical experiments illustrate the superiority of
the proposed numerical scheme compared with standard numerical methods which do
not preserve positivity.
