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@ARTICLE{Kleefeld:1040395,
      author       = {Kleefeld, Andreas and Asante-Asamani, E. O. and Wade, B.
                      A.},
      title        = {{A} fourth-order exponential time differencing scheme with
                      dimensional splitting for non-linear reaction–diffusion
                      systems},
      journal      = {Journal of computational and applied mathematics},
      volume       = {465},
      issn         = {0771-050X},
      address      = {Amsterdam [u.a.]},
      publisher    = {North-Holland},
      reportid     = {FZJ-2025-01875},
      pages        = {116568},
      year         = {2025},
      abstract     = {A fourth-order exponential time differencing (ETD)
                      Runge–Kutta scheme with dimensional splitting is developed
                      to solve multidimensional non-linear systems of
                      reaction–diffusion equations (RDE). By approximating the
                      matrix exponential in the scheme with the A-acceptable Padé
                      (2,2) rational function, the resulting scheme (ETDRK4P22-IF)
                      is verified empirically to be fourth-order accurate for
                      several RDE. The scheme is shown to be more efficient than
                      competing fourth-order ETD and IMEX schemes, achieving up to
                      20X speed-up in CPU time. Inclusion of up to three
                      pre-smoothing steps of a lower order L-stable scheme
                      facilitates efficient damping of spurious oscillations
                      arising from problems with non-smooth initial/boundary
                      conditions.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs)
                      and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5112},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001433835400001},
      doi          = {10.1016/j.cam.2025.116568},
      url          = {https://juser.fz-juelich.de/record/1040395},
}