Dynamical low-rank integrators for second-order matrix differential equations

In this paper, we construct and analyze a new dynamical low-rank integrator for second-order matrix differential equations. The method is based on a combination of the projector-splitting integrator introduced in Lubich and Oseledets (BIT 54(1):171–188, 2014. https://doi.org/10.1007/s10543-013-0454-0 ) and a Strang splitting. We also present a variant of the new integrator which is tailored to semilinear second-order problems.