High degree polynomial interpolation Newton form
SIAM Journal on Scientific and Statistical Computing
Efficient solution of parabolic equations by Krylov approximation methods
SIAM Journal on Scientific and Statistical Computing
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
RKC: an explicit solver for parabolic PDEs
Journal of Computational and Applied Mathematics
Interpolating discrete advection-diffusion propagators at Leja sequences
Journal of Computational and Applied Mathematics
Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems
SIAM Journal on Numerical Analysis
Preconditioning Lanczos Approximations to the Matrix Exponential
SIAM Journal on Scientific Computing
EXPINT---A MATLAB package for exponential integrators
ACM Transactions on Mathematical Software (TOMS)
A parallel exponential integrator for large-scale discretizations of advection-diffusion models
PVM/MPI'05 Proceedings of the 12th European PVM/MPI users' group conference on Recent Advances in Parallel Virtual Machine and Message Passing Interface
Comparing leja and krylov approximations of large scale matrix exponentials
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
An exponential integrator for advection-dominated reactive transport in heterogeneous porous media
Journal of Computational Physics
Exponential Rosenbrock integrators for option pricing
Journal of Computational and Applied Mathematics
ACM Transactions on Mathematical Software (TOMS)
Using the Restricted-denominator Rational Arnoldi Method for Exponential Integrators
SIAM Journal on Matrix Analysis and Applications
New, Highly Accurate Propagator for the Linear and Nonlinear Schrödinger Equation
Journal of Scientific Computing
Comparative performance of exponential, implicit, and explicit integrators for stiff systems of ODEs
Journal of Computational and Applied Mathematics
Exponential Rosenbrock methods of order five - construction, analysis and numerical comparisons
Journal of Computational and Applied Mathematics
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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 and related functions of the Jacobian matrix. To this aim, the Real Leja Points Method is used. It is shown that the properties of this method combine well with the particular requirements of Rosenbrock-type integrators. We verify our implementation with some numerical experiments in MATLAB, where we solve semilinear parabolic PDEs in one and two space dimensions. We further present some numerical experiments in FORTRAN, where we compare our method with other methods from literature. We find a great potential of our method for non-normal matrices. Such matrices typically arise in parabolic problems with large advection in combination with moderate diffusion and mildly stiff reactions.