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 …

Exponential Euler discrete schemes have been widely employed in the studies of Caputo
fractional order differential equations, but almost no literature concerns the Caputo–Fabrizio …

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 …

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

Whether high order temporal integrators can preserve the maximum principle of Allen-Cahn
equation has been an open problem in recent years. This work provides a positive answer …

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 …

Among the fastest methods for solving stiff PDE are exponential integrators, which require
the evaluation of $ f (A) $, where $ A $ is a negative definite matrix and $ f $ is the …

In this paper, we present a variable step size implementation of exponential Rosenbrock-
type methods of orders 2, 3 and 4. These integrators require the evaluation of exponential …

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 paper is concerned with the construction, implementation and numerical analysis of
exponential multistep methods. These methods are related to explicit Adams methods but, in …