In this paper we consider the construction, analysis, implementation and application of
exponential integrators. The focus will be on two types of stiff problems. The first one is …

We give a systematic method for discretizing Hamiltonian partial differential equations
(PDEs) with constant symplectic structure, while preserving their energy exactly. The same …

In the last few decades the concepts of structure-preserving discretization, geometric
integration and compatible discretizations have emerged as subfields in the numerical …

We introduce a new general framework for the approximation of evolution equations at low
regularity and develop a new class of schemes for a wide range of equations under lower …

We introduce low regularity exponential-type integrators for nonlinear Schrödinger
equations for which first-order convergence only requires the boundedness of one …

A novel class of high-order linearly implicit energy-preserving integrating factor Runge–
Kutta methods are proposed for the nonlinear Schrödinger equation. Based on the idea of …

We introduce a numerical framework for dispersive equations embedding their underlying
resonance structure into the discretisation. This will allow us to resolve the nonlinear …

In this paper, combining the ideas of exponential integrators and discrete gradients, we
propose and analyze a new structure-preserving exponential scheme for the conservative or …

We establish optimal error bounds for the exponential wave integrator (EWI) applied to the
nonlinear Schrödinger equation (NLSE) with-potential and/or locally Lipschitz nonlinearity …

This article is concerned with the question of whether it is possible to construct a time
discretization for the one-dimensional cubic nonlinear Schrödinger equation with second …