The exponential accuracy of Fourier and Chebyshev differencing methods
SIAM Journal on Numerical Analysis
Spectral methods in time for parabolic problems
SIAM Journal on Numerical Analysis
Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
A first course in the numerical analysis of differential equations
A first course in the numerical analysis of differential equations
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
Spectral methods in MatLab
Exponential time differencing for stiff systems
Journal of Computational Physics
Computing a matrix function for exponential integrators
Journal of Computational and Applied Mathematics
Fourth-Order Time-Stepping for Stiff PDEs
SIAM Journal on Scientific Computing
The Scaling and Squaring Method for the Matrix Exponential Revisited
SIAM Journal on Matrix Analysis and Applications
Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
EXPINT---A MATLAB package for exponential integrators
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
An error analysis of the modified scaling and squaring method
Computers & Mathematics with Applications
The scaling and modified squaring method for matrix functions related to the exponential
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
The scaling and modified squaring method for matrix functions related to the exponential
Applied Numerical Mathematics
Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation
Journal of Computational Physics
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We compare six different categories of numerical methods for the evaluation of functions of the matrix exponential. These functions are required for exponential integrators, and are not straightforward to evaluate because they are highly susceptible to rounding errors when the matrix has small eigenvalues. The comparison takes into account both accuracy and computational time. A scaling and squaring algorithm and a diagonalisation algorithm are both found to be efficient.