  We consider strong convergence of the finite differences approximation in
space for stochastic reaction diffusion equations with multiplicative noise
under a one-sided Lipschitz condition only. We derive convergence with an
implicit rate depending on the regularity of the exact solution. This can be
made explicit if the variational solution has more than its canonical spatial
regularity. As an application, spatially extended FitzHugh-Nagumo systems with
noise are considered.
