41 citations · 329 across the 23 of their papers we have counts for
29 papers
On energy conservation by trigonometric integrators in the linear case with application to wave equations
Ludwig Gauckler
Trigonometric integrators for oscillatory linear Hamiltonian differential equations are considered. Under a condition of Hairer & Lubich on the filter functions in the method, a mo…
High-order splitting integrators for nonlinear Schrödinger equations over long times
Ludwig Gauckler
The long-time behaviour of splitting integrators applied to nonlinear Schrödinger equations in a weakly nonlinear setting is studied. It is proven that the energy is nearly conserv…
Dynamics, numerical analysis, and some geometry
Ludwig Gauckler, Ernst Hairer, Christian Lubich
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 equation…
Trigonometric integrators for quasilinear wave equations
Ludwig Gauckler, Jianfeng Lu, Jeremy L. Marzuola +2
Trigonometric time integrators are introduced as a class of explicit numerical methods for quasilinear wave equations. Second-order convergence for the semi-discretization in time…
On a splitting method for the Zakharov system
Ludwig Gauckler
An error analysis of a splitting method applied to the Zakharov system is given. The numerical method is a Lie-Trotter splitting in time that is combined with a Fourier collocation…
Metastable energy strata in numerical discretizations of weakly nonlinear wave equations
Ludwig Gauckler, Daniel Weiss
The quadratic nonlinear wave equation on a one-dimensional torus with small initial values located in a single Fourier mode is considered. In this situation, the formation of metas…