Dynamics, numerical analysis, and some geometry
Ludwig Gauckler, Ernst Hairer and Christian Lubich
Abstract. Geometric aspects play an important role in the
construction and analysis of structure-preserving numerical methods
for a wide variety of ordinary and partial differential equations.
Here we review the development and theory of symplectic integrators
for Hamiltonian ordinary and partial differential equations,
of dynamical low-rank approximation of time-dependent large
matrices and tensors, and its use in numerical integrators for
Hamiltonian tensor network approximations in quantum dynamics.
Key Words. Geometric numerical integration, symplectic integrators,
dynamical low-rank approximation, Hamiltonian tensor network approximations.