  We introduce free probability analogues of the stochastic theta methods for
free stochastic differential equations in this work. Under some mild
conditions, we prove the strong convergence and exponential stability in mean
square of the numerical methods. The free stochastic theta method with
$\theta=1$ can inherit the exponential stability of original equations for any
given step size. Our method offers better stability and efficiency than the
free Euler-Maruyama method. Moreover, numerical results are reported to confirm
these theoretical findings.
