We study a semi-implicit time-difference scheme for magnetohydrodynamics of a viscous
and resistive incompressible fluid in a bounded smooth domain with a perfectly conducting boundary.
In the scheme, the velocity and magnetic fields are updated by solving simple Helmholtz equations.
Pressure is treated explicitly in time, by solving Poisson equations corresponding to a recently de-
veloped formula for the Navier-Stokes pressure involving the commutator of Laplacian and Leray
projection operators. We prove stability of the time-difference scheme, and deduce a local-time well-
posedness theorem for MHD dynamics extended to ignore the divergence-free constraint on velocity
and magnetic fields. These fields are divergence-free for all later time if they are initially so.