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. Boito, Paola; Eidelman, Yuli; Gemignani, Luca: Computing the reciprocal of a (\phi)-function by rational approximation (2022)
  2. Li, Dongping; Yang, Siyu; Lan, Jiamei: Efficient and accurate computation for the (\varphi)-functions arising from exponential integrators (2022)
  3. Muñoz-Matute, Judit; Demkowicz, Leszek; Pardo, David: Error representation of the time-marching DPG scheme (2022)
  4. Wang, Bin; Jiang, Yaolin: Optimal convergence and long-time conservation of exponential integration for Schrödinger equations in a normal or highly oscillatory regime (2022)
  5. Botchev, Mike A.; Knizhnerman, Leonid; Tyrtyshnikov, Eugene E.: Residual and restarting in Krylov subspace evaluation of the (\varphi) function (2021)
  6. Luan, Vu Thai: Efficient exponential Runge-Kutta methods of high order: construction and implementation (2021)
  7. Muñoz-Matute, Judit; Pardo, David; Demkowicz, Leszek: A DPG-based time-marching scheme for linear hyperbolic problems (2021)
  8. Muñoz-Matute, Judit; Pardo, David; Demkowicz, Leszek: Equivalence between the DPG method and the exponential integrators for linear parabolic problems (2021)
  9. Naranjo-Noda, F. S.; Jimenez, J. C.: Locally linearized Runge-Kutta method of Dormand and Prince for large systems of initial value problems (2021)
  10. Buvoli, Tommaso: A class of exponential integrators based on spectral deferred correction (2020)
  11. Jimenez, J. C.; de la Cruz, H.; De Maio, P. A.: Efficient computation of phi-functions in exponential integrators (2020)
  12. Montanelli, Hadrien; Bootland, Niall: Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators (2020)
  13. Narayanamurthi, Mahesh; Tranquilli, Paul; Sandu, Adrian; Tokman, Mayya: EPIRK-(W) and EPIRK-(K) time discretization methods (2019)
  14. Gheorghiu, Călin-Ioan: Spectral collocation solutions to problems on unbounded domains (2018)
  15. Isherwood, Leah; Grant, Zachary J.; Gottlieb, Sigal: Strong stability preserving integrating factor Runge-Kutta methods (2018)
  16. Botchev, Mikhail A.: Krylov subspace exponential time domain solution of Maxwell’s equations in photonic crystal modeling (2016)
  17. Cousins, Will; Sapsis, Themistoklis P.: Reduced-order precursors of rare events in unidirectional nonlinear water waves (2016)
  18. Li, Yu-Wen; Wu, Xinyuan: Exponential integrators preserving first integrals or Lyapunov functions for conservative or dissipative systems (2016)
  19. Weiner, Rüdiger; Bruder, Jürgen: Exponential Krylov peer integrators (2016)
  20. Wu, Gang; Zhang, Lu; Xu, Ting-ting: A framework of the harmonic Arnoldi method for evaluating (\varphi)-functions with applications to exponential integrators (2016)

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