Recently, a great deal of attention has been focused on the construction of exponential integrators for semilinear problems. In this article we describe a MATLAB package which aims to facilitate the quick deployment and testing of exponential integrators, of Runge--Kutta, multistep, and general linear type. A large number of integrators are included in this package along with several well-known examples. The so-called ϕ functions and their evaluation is crucial for accuracy, stability, and efficiency of exponential integrators, and the approach taken here is through a modification of the scaling and squaring technique, the most common approach used for computing the matrix exponential.

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  1. Botchev, Mikhail A.: Krylov subspace exponential time domain solution of Maxwell’s equations in photonic crystal modeling (2016)
  2. Li, Yu-Wen; Wu, Xinyuan: Exponential integrators preserving first integrals or Lyapunov functions for conservative or dissipative systems (2016)
  3. Weiner, Rüdiger; Bruder, Jürgen: Exponential Krylov peer integrators (2016)
  4. Wu, Gang; Zhang, Lu; Xu, Ting-ting: A framework of the harmonic Arnoldi method for evaluating $\varphi$-functions with applications to exponential integrators (2016)
  5. Cano, B.; González-Pachón, A.: Exponential time integration of solitary waves of cubic Schrödinger equation (2015)
  6. Whalen, P.; Brio, M.; Moloney, J.V.: Exponential time-differencing with embedded Runge-Kutta adaptive step control (2015)
  7. Cousins, Will; Sapsis, Themistoklis P.: Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model (2014)
  8. Grooms, Ian G.; Majda, Andrew J.: Stochastic superparameterization in a one-dimensional model for wave turbulence (2014)
  9. Carr, E.J.; Turner, I.W.; Perré, P.: A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media: application to wood drying (2013)
  10. Carroll, John; O’Callaghan, Eoin: Exponential almost Runge-Kutta methods for semilinear problems (2013)
  11. Gander, Martin J.; Güttel, Stefan: PARAEXP: a parallel integrator for linear initial-value problems (2013)
  12. Korzec, M.D.; Ahnert, T.: Time-stepping methods for the simulation of the self-assembly of nano-crystals in MATLAB on a GPU (2013)
  13. Geiger, Sebastian; Lord, Gabriel; Tambue, Antoine: Exponential time integrators for stochastic partial differential equations in 3D reservoir simulation (2012)
  14. Momoniat, E.: Matrix exponentiation and the Frank-Kamenetskii equation (2012)
  15. Weiner, Rüdiger; El-Azab, Tamer: Exponential peer methods (2012)
  16. Carr, E.J.; Moroney, T.J.; Turner, I.W.: Efficient simulation of unsaturated flow using exponential time integration (2011)
  17. Garrappa, Roberto; Popolizio, Marina: On accurate product integration rules for linear fractional differential equations (2011)
  18. Garrappa, Roberto; Popolizio, Marina: Generalized exponential time differencing methods for fractional order problems (2011)
  19. Grooms, Ian; Julien, Keith: Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation (2011)
  20. Ashi, H.A.; Cummings, L.J.; Matthews, P.C.: Exponential time differencing methods: stability analysis and application to the nonlinear Schrödinger equation (2010)

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Further publications can be found at: http://www.math.ntnu.no/num/expint/publications.php