Runge-Kutta approximation of quasi-linear parabolic equations
Mathematics of Computation
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
Exponential Integrators for Large Systems of Differential Equations
SIAM Journal on Scientific Computing
Exponential time differencing for stiff systems
Journal of Computational Physics
Commutator-free Lie group methods
Future Generation Computer Systems - Special issue: Geometric numerical algorithms
Journal of Computational and Applied Mathematics
An error analysis of the modified scaling and squaring method
Computers & Mathematics with Applications
On the construction of restricted-denominator exponential W-methods
Journal of Computational and Applied Mathematics
A rational Krylov method for solving time-periodic differential equations
Applied Numerical 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
Exponential Runge--Kutta methods for the Schrödinger equation
Applied Numerical Mathematics
Exponential Runge-Kutta methods for delay differential equations
Mathematics and Computers in Simulation
Comparing leja and krylov approximations of large scale matrix exponentials
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
Reprint of "Explicit exponential Runge-Kutta methods of high order for parabolic problems"
Journal of Computational and Applied Mathematics
Hi-index | 0.00 |
The aim of this paper is to construct exponential Runge-Kutta methods of collocation type and to analyze their convergence properties for linear and semilinear parabolic problems. For the analysis, an abstract Banach space framework of sectorial operators and locally Lipschitz continuous nonlinearities is chosen. This framework includes interesting examples like reaction-diffusion equations. It is shown that the methods converge at least with their stage order, and that convergence of higher order (up to the classical order) occurs, if the problem has sufficient temporal and spatial smoothness. The latter, however, might require the source function to fulfil unnatural boundary conditions. Therefore, the classical order is not always obtained and an order reduction must be expected, in general.