Efficient solution of parabolic equations by Krylov approximation methods
SIAM Journal on Scientific and Statistical Computing
A new class of time discretization schemes for the solution of nonlinear PDEs
Journal of Computational Physics
Exponential time differencing for stiff systems
Journal of Computational Physics
On the numerical inversion of the Laplace transform of certain holomorphic mappings
Applied Numerical Mathematics
Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems
SIAM Journal on Numerical Analysis
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
A Spectral Order Method for Inverting Sectorial Laplace Transforms
SIAM Journal on Numerical Analysis
EXPINT---A MATLAB package for exponential integrators
ACM Transactions on Mathematical Software (TOMS)
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
On linear stability of predictor-corrector algorithms for fractional differential equations
International Journal of Computer Mathematics
On accurate product integration rules for linear fractional differential equations
Journal of Computational and Applied Mathematics
Evaluation of generalized Mittag---Leffler functions on the real line
Advances in Computational Mathematics
A family of Adams exponential integrators for fractional linear systems
Computers & Mathematics with Applications
Mathematics and Computers in Simulation
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The main aim of this paper is to discuss the generalization of exponential integrators to differential equations of non-integer orders. Two methods of this kind are devised and the accuracy and stability are investigated. Some numerical experiments are presented to validate the theoretical findings.