Exponential integrators
M Hochbruck, A Ostermann - Acta Numerica, 2010 - cambridge.org
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 integrators. The focus will be on two types of stiff problems. The first one is …
Global exponential stability of discrete-time almost automorphic Caputo–Fabrizio BAM fuzzy neural networks via exponential Euler technique
T Zhang, Y Li - Knowledge-Based Systems, 2022 - Elsevier
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 …
fractional order differential equations, but almost no literature concerns the Caputo–Fabrizio …
Exponential Rosenbrock-type methods
M Hochbruck, A Ostermann, J Schweitzer - SIAM Journal on Numerical …, 2009 - SIAM
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 …
scale systems of stiff differential equations. These so-called Rosenbrock-type methods …
Topics in structure-preserving discretization
In the last few decades the concepts of structure-preserving discretization, geometric
integration and compatible discretizations have emerged as subfields in the numerical …
integration and compatible discretizations have emerged as subfields in the numerical …
Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation
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 …
equation has been an open problem in recent years. This work provides a positive answer …
EXPINT---A MATLAB package for exponential integrators
H Berland, B Skaflestad, WM Wright - ACM Transactions on …, 2007 - dl.acm.org
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 …
integrators for semilinear problems. In this article we describe a MATLAB1 package which …
Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals
T Schmelzer, L Trefethen - 2006 - ora.ox.ac.uk
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 …
the evaluation of $ f (A) $, where $ A $ is a negative definite matrix and $ f $ is the …
Implementation of exponential Rosenbrock-type integrators
M Caliari, A Ostermann - Applied Numerical Mathematics, 2009 - Elsevier
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 …
type methods of orders 2, 3 and 4. These integrators require the evaluation of exponential …
[HTML][HTML] Comparative performance of exponential, implicit, and explicit integrators for stiff systems of ODEs
J Loffeld, M Tokman - Journal of Computational and Applied Mathematics, 2013 - Elsevier
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 …
still limited understanding of how their performance compares with that of state-of-the-art …
Exponential multistep methods of Adams-type
M Hochbruck, A Ostermann - BIT Numerical Mathematics, 2011 - Springer
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 …
exponential multistep methods. These methods are related to explicit Adams methods but, in …