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 …
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 …
Algorithm 919: A Krylov subspace algorithm for evaluating the ϕ-functions appearing in exponential integrators
J Niesen, WM Wright - ACM Transactions on Mathematical Software …, 2012 - dl.acm.org
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 …
differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to …
Relaxation exponential Rosenbrock-type methods for oscillatory Hamiltonian systems
D Li, X Li - SIAM Journal on Scientific Computing, 2023 - SIAM
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 …
the problems and the requirement of highly stable and energy-preserving schemes. The …
Fourth-order compact schemes for the numerical simulation of coupled Burgers' equation
HP Bhatt, AQM Khaliq - Computer Physics Communications, 2016 - Elsevier
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 …
Kutta (ETDRK) schemes in combination with a global fourth-order compact finite difference …
KIOPS: A fast adaptive Krylov subspace solver for exponential integrators
S Gaudreault, G Rainwater, M Tokman - Journal of Computational Physics, 2018 - Elsevier
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 …
functions that appear in exponential integrators. This algorithm is suitable for large-scale …
[HTML][HTML] Building blocks needed for mechanistic modeling of bioprocesses: A critical review based on protein production by CHO cells
Y González-Hernández, P Perré - Metabolic Engineering Communications, 2024 - Elsevier
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 …
as an operational production tool. The Chinese Hamster Ovary (CHO) cell, one of the most …
[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 …
BAMPHI: Matrix-free and transpose-free action of linear combinations of φ-functions from exponential integrators
M Caliari, F Cassini, F Zivcovich - Journal of Computational and Applied …, 2023 - Elsevier
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 …
from the spatial discretization of Partial Differential Equations (PDEs), constitutes a hot topic …
[HTML][HTML] Exponential Rosenbrock methods of order five—construction, analysis and numerical comparisons
VT Luan, A Ostermann - Journal of Computational and Applied …, 2014 - Elsevier
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 …
analyze their convergence properties for the time discretization of large-scale systems of stiff …