  Studying the propagation of uncertainties in a nonlinear dynamical system
usually involves generating a set of samples in the stochastic parameter space
and then repeated simulations with different sampled parameters. The main
difficulty faced in the process is the excessive computational cost. In this
paper, we present an efficient, partitioned ensemble algorithm to determine
multiple realizations of a reduced Magnetohydrodynamics (MHD) system, which
models MHD flows at low magnetic Reynolds number. The algorithm decouples the
fully coupled problem into two smaller sub-physics problems, which reduces the
size of the linear systems that to be solved and allows the use of optimized
codes for each sub-physics problem. Moreover, the resulting coefficient
matrices are the same for all realizations at each time step, which allows
faster computation of all realizations and significant savings in computational
cost. We prove this algorithm is first order accurate and long time stable
under a time step condition. Numerical examples are provided to verify the
theoretical results and demonstrate the efficiency of the algorithm.
