Journal of Computational and Applied Mathematics
A method for exponential propagation of large systems of stiff nonlinear differential equations
Journal of Scientific Computing
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
ROWMAP—a ROW-code with Krylov techniques for large stiff ODEs
Applied Numerical Mathematics - Special issue on time integration
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
Order results for Krylov-W-methods
Computing
Exponential Integrators for Large Systems of Differential Equations
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
The Scaling and Squaring Method for the Matrix Exponential Revisited
SIAM Journal on Matrix Analysis and Applications
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Journal of Computational Physics
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
Journal of Computational and Applied Mathematics
Exponential Rosenbrock-Type Methods
SIAM Journal on Numerical Analysis
A New Scaling and Squaring Algorithm for the Matrix Exponential
SIAM Journal on Matrix Analysis and Applications
A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK)
Journal of Computational Physics
Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
SIAM Journal on Scientific Computing
Hi-index | 7.29 |
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 integrators, most notably the commonly used Newton-Krylov implicit methods. In this paper we present comparative performance analysis of Krylov-based exponential, implicit and explicit integrators on a suite of stiff test problems and demonstrate that exponential integrators have computational advantages compared to the other methods, particularly as problems become larger and more stiff. We argue that the faster convergence of the Krylov iteration within exponential integrators accounts for the main proportion of the computational savings that they provide and illustrate how the structure of these methods ensures such efficiency. In addition, we demonstrate the computational advantages of the newly introduced Tokman and Loffeld (2010) [17] exponential propagation Runge-Kutta (EpiRK) fifth-order methods. The detailed analysis of the performance of the methods that is presented provides guidelines for the construction and implementation of efficient exponential methods and the quantitative comparisons inform the selection of appropriate schemes for other problems.