Expokit: a software package for computing matrix exponentials
ACM Transactions on Mathematical Software (TOMS)
Design, analysis and testing of some parallel two-step W-methods for stiff systems
Applied Numerical Mathematics
Extrapolation in lie groups with approximated BCH-formula
Applied Numerical Mathematics
Complexity theory for lie-group solvers
Journal of Complexity
A composite Runge-Kutta method for the spectral solution of semilinear PDEs
Journal of Computational Physics
Applied Mathematics and Computation
ParNum '99 Proceedings of the 4th International ACPC Conference Including Special Tracks on Parallel Numerics and Parallel Computing in Image Processing, Video Processing, and Multimedia: Parallel Computation
New vector forms of elemental functions with Taylor series
Applied Mathematics and Computation
Computing a matrix function for exponential integrators
Journal of Computational and Applied Mathematics
Parallel 'Peer' two-step W-methods and their application to MOL-systems
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Construction of highly stable two-step W-methods for ordinary differential equations
Journal of Computational and Applied Mathematics
Interpolating discrete advection-diffusion propagators at Leja sequences
Journal of Computational and Applied Mathematics
The Gautschi time stepping scheme for edge finite element discretizations of the Maxwell equations
Journal of Computational Physics
EXPINT---A MATLAB package for exponential integrators
ACM Transactions on Mathematical Software (TOMS)
Exponential Runge-Kutta methods for parabolic problems
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Krylov-ROW methods for DAEs of index 1 with applications to viscoelasticity
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Journal of Computational Physics
An error analysis of the modified scaling and squaring method
Computers & Mathematics with Applications
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
A rational Krylov method for solving time-periodic differential equations
Applied Numerical Mathematics
Smoothing schemes for reaction-diffusion systems with nonsmooth data
Journal of Computational and Applied Mathematics
Application of operator splitting to the Maxwell equations including a source term
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
Journal of Computational and Applied Mathematics
Parallel solution of the chemical master equation
SpringSim '09 Proceedings of the 2009 Spring Simulation Multiconference
Exponential Runge--Kutta methods for parabolic problems
Applied Numerical Mathematics
Krylov-ROW methods for DAEs of index 1 with applications to viscoelasticity
Applied Numerical Mathematics
A survey on methods for computing matrix exponentials in numerical schemes for ODEs
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartII
Development and acceleration of parallel chemical transport models
SpringSim '10 Proceedings of the 2010 Spring Simulation Multiconference
Approximation of Semigroups and Related Operator Functions by Resolvent Series
SIAM Journal on Numerical Analysis
Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation
Journal of Computational Physics
A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK)
Journal of Computational Physics
Computing $f(A)b$ via Least Squares Polynomial Approximations
SIAM Journal on Scientific Computing
Exponential Runge-Kutta Methods for Stiff Kinetic Equations
SIAM Journal on Numerical Analysis
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
Local linearization-runge kutta (LLRK) methods for solving ordinary differential equations
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
ACM Transactions on Mathematical Software (TOMS)
Communication-Efficient algorithms for numerical quantum dynamics
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Using the Restricted-denominator Rational Arnoldi Method for Exponential Integrators
SIAM Journal on Matrix Analysis and Applications
Applied Numerical Mathematics
Computation of matrix functions with deflated restarting
Journal of Computational and Applied Mathematics
Comparative performance of exponential, implicit, and explicit integrators for stiff systems of ODEs
Journal of Computational and Applied Mathematics
Exponential integrators for stiff elastodynamic problems
ACM Transactions on Graphics (TOG)
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
Journal of Scientific Computing
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
A comparison of AMF- and Krylov-methods in Matlab for large stiff ODE systems
Journal of Computational and Applied Mathematics
Journal of Computational Physics
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We study the numerical integration of large stiff systems of differential equations by methods that use matrix--vector products with the exponential or a related function of the Jacobian. For large problems, these can be approximated by Krylov subspace methods, which typically converge faster than those for the solution of the linear systems arising in standard stiff integrators. The exponential methods also offer favorable properties in the integration of differential equations whose Jacobian has large imaginary eigenvalues. We derive methods up to order 4 which are exact for linear constant-coefficient equations. The implementation of the methods is discussed. Numerical experiments with reaction-diffusion problems and a time-dependent Schrödinger equation are included.