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. Buvoli, Tommaso: A class of exponential integrators based on spectral deferred correction (2020)
  2. Jimenez, J. C.; de la Cruz, H.; De Maio, P. A.: Efficient computation of phi-functions in exponential integrators (2020)
  3. Narayanamurthi, Mahesh; Tranquilli, Paul; Sandu, Adrian; Tokman, Mayya: EPIRK-(W) and EPIRK-(K) time discretization methods (2019)
  4. Gheorghiu, Călin-Ioan: Spectral collocation solutions to problems on unbounded domains (2018)
  5. Isherwood, Leah; Grant, Zachary J.; Gottlieb, Sigal: Strong stability preserving integrating factor Runge-Kutta methods (2018)
  6. Botchev, Mikhail A.: Krylov subspace exponential time domain solution of Maxwell’s equations in photonic crystal modeling (2016)
  7. Cousins, Will; Sapsis, Themistoklis P.: Reduced-order precursors of rare events in unidirectional nonlinear water waves (2016)
  8. Li, Yu-Wen; Wu, Xinyuan: Exponential integrators preserving first integrals or Lyapunov functions for conservative or dissipative systems (2016)
  9. Weiner, Rüdiger; Bruder, Jürgen: Exponential Krylov peer integrators (2016)
  10. Wu, Gang; Zhang, Lu; Xu, Ting-ting: A framework of the harmonic Arnoldi method for evaluating (\varphi)-functions with applications to exponential integrators (2016)
  11. Cano, B.; González-Pachón, A.: Exponential time integration of solitary waves of cubic Schrödinger equation (2015)
  12. Whalen, P.; Brio, M.; Moloney, J. V.: Exponential time-differencing with embedded Runge-Kutta adaptive step control (2015)
  13. Cousins, Will; Sapsis, Themistoklis P.: Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model (2014)
  14. Grooms, Ian G.; Majda, Andrew J.: Stochastic superparameterization in a one-dimensional model for wave turbulence (2014)
  15. Botchev, M. A.: A block Krylov subspace time-exact solution method for linear ordinary differential equation systems. (2013)
  16. 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)
  17. Carroll, John; O’Callaghan, Eoin: Exponential almost Runge-Kutta methods for semilinear problems (2013)
  18. Gander, Martin J.; Güttel, Stefan: PARAEXP: a parallel integrator for linear initial-value problems (2013)
  19. Korzec, M. D.; Ahnert, T.: Time-stepping methods for the simulation of the self-assembly of nano-crystals in MATLAB on a GPU (2013)
  20. Geiger, Sebastian; Lord, Gabriel; Tambue, Antoine: Exponential time integrators for stochastic partial differential equations in 3D reservoir simulation (2012)

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