Before revision: We develop a new class of algorithms, which we call step-truncation methods, to integrate in time an initial value problem for an ODE or a PDE on a low-rank tensor manifold. The new methods are based on performing a time step with a conventional time-stepping scheme  followed by a truncation operation into a tensor manifold with prescribed rank.
After revision: We develop a new class of algorithms, which we call step-truncation methods, are based on performing a time step with a conventional time-stepping scheme followed by a truncation operation into a tensor manifold with prescribed rank.