Journal of Computational and Applied Mathematics
A method for exponential propagation of large systems of stiff nonlinear differential equations
Journal of Scientific Computing
Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
Calculation of functions of unsymmetric matrices using Arnoldi's method
Computational Mathematics and Mathematical Physics
Efficient solution of parabolic equations by Krylov approximation methods
SIAM Journal on Scientific and Statistical Computing
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Expokit: a software package for computing matrix exponentials
ACM Transactions on Mathematical Software (TOMS)
A new class of time discretization schemes for the solution of nonlinear PDEs
Journal of Computational Physics
An exponential method of numerical integration of ordinary differential equations
Communications of the ACM
Exponential time differencing for stiff systems
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Fourth-Order Time-Stepping for Stiff PDEs
SIAM Journal on Scientific Computing
Generalized integrating factor methods for stiff PDEs
Journal of Computational Physics
Exponential Runge--Kutta methods for parabolic problems
Applied Numerical Mathematics
Simulation and verification for computational modelling of signalling pathways
Proceedings of the 38th conference on Winter simulation
An iterative semi-implicit scheme with robust damping
Journal of Computational Physics
Comparison of methods for evaluating functions of a matrix exponential
Applied Numerical Mathematics
The scaling and modified squaring method for matrix functions related to the exponential
Applied Numerical Mathematics
A massively parallel exponential integrator for advection-diffusion models
Journal of Computational and Applied Mathematics
A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK)
Journal of Computational Physics
Using the Restricted-denominator Rational Arnoldi Method for Exponential Integrators
SIAM Journal on Matrix Analysis and Applications
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
Hi-index | 31.46 |
A new class of exponential propagation techniques which we call exponential propagation iterative (EPI) methods is introduced in this paper. It is demonstrated how for large stiff systems these schemes provide an efficient alternative to standard integrators for computing solutions over long time intervals. The EPI methods are constructed by reformulating the integral form of a solution to a nonlinear autonomous system of ODEs as an expansion in terms of products between special functions of matrices and vectors that can be efficiently approximated using Krylov subspace projections. The methodology for constructing EPI schemes is presented and their performance is illustrated using numerical examples and comparisons with standard explicit and implicit integrators. The history of the exponential propagation type integrators and their connection with EPI schemes are also discussed.