Recently, there has been a great deal of interest in the construction of exponential
integrators. These integrators, as their name suggests, use the exponential function (and …

The aim of this paper is to analyze explicit exponential Runge--Kutta methods for the time
integration of semilinear parabolic problems. The analysis is performed in an abstract …

Recently, a great deal of attention has been focused on the construction of exponential
integrators for semilinear problems. In this article we describe a MATLAB1 package which …

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

Symplecticity is also an important property for exponential Runge–Kutta (ERK) methods in
the sense of structure preservation once the underlying problem is a Hamiltonian system …

As one of the most important properties, energy preservation is a natural requirement for
numerical integrators of Hamiltonian systems. Considering the limited second-order …

We propose a new class of the exponential propagation iterative methods of Runge–Kutta-
type (EPIRK). The EPIRK schemes are exponential integrators that can be competitive with …

The solution of a parabolic stochastic partial differential equation (SPDE) driven by an
infinite-dimensional Brownian motion is in general not a semi-martingale anymore and does …

In this paper, extended Runge–Kutta–Nyström-type methods for the numerical integration of
perturbed oscillators with low frequencies are presented, which inherit the framework of …

Exponential Runge--Kutta (ERK) and partitioned exponential Runge--Kutta (PERK) methods
are developed for solving initial value problems with vector fields that can be split into …