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 introduce a new class of exponential integrators for the numerical integration of large-
scale systems of stiff differential equations. These so-called Rosenbrock-type methods …

We develop an algorithm for computing the solution of a large system of linear ordinary
differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to …

It is challenging to numerically solve oscillatory Hamiltonian systems due to the stiffness of
the problems and the requirement of highly stable and energy-preserving schemes. The …

This paper introduces two new modified fourth-order exponential time differencing Runge–
Kutta (ETDRK) schemes in combination with a global fourth-order compact finite difference …

This paper presents a new algorithm KIOPS for computing linear combinations of φ-
functions that appear in exponential integrators. This algorithm is suitable for large-scale …

This paper reviews the key building blocks needed to develop a mechanistic model for use
as an operational production tool. The Chinese Hamster Ovary (CHO) cell, one of the most …

Exponential integrators have enjoyed a resurgence of interest in recent years, but there is
still limited understanding of how their performance compares with that of state-of-the-art …

The time integration of stiff systems of Ordinary Differential Equations (ODEs), usually arising
from the spatial discretization of Partial Differential Equations (PDEs), constitutes a hot topic …

The aim of this paper is to construct high-order exponential Rosenbrock methods and to
analyze their convergence properties for the time discretization of large-scale systems of stiff …