  In this paper, we consider numerical approximations for solving the
inductionless magnetohydrodynamic (MHD) equations. By utilizing the scalar
auxiliary variable (SAV) approach for dealing with the convective and coupling
terms, we propose some first- and second-order schemes for this system. These
schemes are linear, decoupled, unconditionally energy stable, and only require
solving a sequence of differential equations with constant coefficients at each
time step. We further derive a rigorous error analysis for the first-order
scheme, establishing optimal convergence rates for the velocity, pressure,
current density and electric potential in the two-dimensional case. Numerical
examples are presented to verify the theoretical findings and show the
performances of the schemes.
