Rank-adaptive dynamical low-rank integrators for first-order and second-order matrix differential equations

Abstract Dynamical low-rank integrators for matrix differential equations recently attracted a lot of attention and have proven to be very efficient in various applications. In this paper, we propose novel strategy choosing the rank projector-splitting integrator Lubich Oseledets adaptively. It is based on combination error estimators local time-discretization with aim balance both. This ensures that convergence underlying time preserved. The adaptive algorithm works methods first-order also dynamical second-order equations, which use method its substeps. Numerical experiments illustrate performance new integrators.