  In this work, we develop a multi-factor approximation for Stochastic Volterra
Equations with Lipschitz coefficients and kernels of completely monotone type
that may be singular. Our approach consists in truncating and then discretizing
the integral defining the kernel, which corresponds to a classical Stochastic
Differential Equation. We prove strong convergence results for this
approximation. For the particular rough kernel case with Hurst parameter lying
in $(0,1/2)$, we propose various discretization procedures and give their
precise rates of convergence. We illustrate the efficiency of our approximation
schemes with numerical tests for the rough Bergomi model.
