EXPINT---A MATLAB package for exponential integrators
ACM Transactions on Mathematical Software (TOMS)
Applied Numerical Mathematics
Journal of Computational Physics
The LEM exponential integrator for advection-diffusion-reaction equations
Journal of Computational and Applied Mathematics
On the construction of restricted-denominator exponential W-methods
Journal of Computational and Applied Mathematics
Lie group integrators with non-autonomous frozen vector fields
International Journal of Computational Science and Engineering
Approximation of matrix operators applied to multiple vectors
Mathematics and Computers in Simulation
Comparison of methods for evaluating functions of a matrix exponential
Applied Numerical Mathematics
Implementation of exponential Rosenbrock-type integrators
Applied Numerical Mathematics
The scaling and modified squaring method for matrix functions related to the exponential
Applied Numerical Mathematics
A New Class of Highly Accurate Solvers for Ordinary Differential Equations
Journal of Scientific Computing
Exponential Runge--Kutta methods for the Schrödinger equation
Applied Numerical Mathematics
A massively parallel exponential integrator for advection-diffusion models
Journal of Computational and Applied Mathematics
Exponential Rosenbrock integrators for option pricing
Journal of Computational and Applied Mathematics
Order conditions for Volterra Runge--Kutta methods
Applied Numerical Mathematics
Exponential Runge-Kutta methods for delay differential equations
Mathematics and Computers in Simulation
Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation
Journal of Computational Physics
Generalized exponential time differencing methods for fractional order problems
Computers & Mathematics with Applications
A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK)
Journal of Computational Physics
Exponential Runge-Kutta Methods for Stiff Kinetic Equations
SIAM Journal on Numerical Analysis
Integrating factor methods as exponential integrators
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Fourth Order Time-Stepping for Kadomtsev-Petviashvili and Davey-Stewartson Equations
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
New, Highly Accurate Propagator for the Linear and Nonlinear Schrödinger Equation
Journal of Scientific Computing
High-order symmetric multistep cosine methods
Applied Numerical Mathematics
Time-stepping methods for the simulation of the self-assembly of nano-crystals in Matlab on a GPU
Journal of Computational Physics
Explicit exponential Runge-Kutta methods of high order for parabolic problems
Journal of Computational and Applied Mathematics
Exponential Rosenbrock methods of order five - construction, analysis and numerical comparisons
Journal of Computational and Applied Mathematics
Exponential Runge-Kutta for the inhomogeneous Boltzmann equations with high order of accuracy
Journal of Computational Physics
Reprint of "Explicit exponential Runge-Kutta methods of high order for parabolic problems"
Journal of Computational and Applied Mathematics
Error analysis of explicit TSERKN methods for highly oscillatory systems
Numerical Algorithms
Hi-index | 0.03 |
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 Banach space framework of sectorial operators and locally Lipschitz continuous nonlinearities. We commence by giving a new and short derivation of the classical (nonstiff) order conditions for exponential Runge--Kutta methods, but the main interest of our paper lies in the stiff case. By expanding the errors of the numerical method in terms of the solution, we derive new order conditions that form the basis of our error bounds for parabolic problems. We show convergence for methods up to order four, and we analyze methods that were recently presented in the literature. These methods have classical order four, but they do not satisfy some of the new conditions. Therefore, an order reduction is expected. We present numerical experiments which show that this order reduction in fact arises in practical examples. Based on our new conditions, we finally construct methods that do not suffer from order reduction.