Before revision:  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. By considering such truncation operation as a nonlinear operator in the space of tensors , we prove various consistency results and errors estimates for a wide range of step-truncation algorithms.
After revision:  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 . By selecting the rank of the tensor manifold adaptively to satisfy stability and accuracy requirements , we prove various consistency results and errors estimates for a wide range of step-truncation algorithms.