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@ARTICLE{Baumann:1034860,
      author       = {Baumann, Thomas and Götschel, Sebastian and Lunet, Thibaut
                      and Ruprecht, Daniel and Speck, Robert},
      title        = {{A}daptive time step selection for spectral deferred
                      correction},
      journal      = {Numerical algorithms},
      volume       = {100},
      issn         = {1017-1398},
      publisher    = {Springer Science Business Media B.V.},
      reportid     = {FZJ-2024-07607},
      pages        = {369-393},
      year         = {2025},
      abstract     = {Spectral Deferred Correction (SDC) is an iterative method
                      for the numerical solution of ordinary differential
                      equations. It works by refining the numerical solution for
                      an initial value problem by approximately solving
                      differential equations for the error, and can be interpreted
                      as a preconditioned fixed-point iteration for solving the
                      fully implicit collocation problem. We adopt techniques from
                      embedded Runge-Kutta Methods (RKM) to SDC in order to
                      provide a mechanism for adaptive time step size selection
                      and thus increase computational efficiency of SDC. We
                      propose two SDC-specific estimates of the local error that
                      are generic and do not rely on problem specific quantities.
                      We demonstrate a gain in efficiency over standard SDC with
                      fixed step size and compare efficiency favorably against
                      state-of-the-art adaptive RKM.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs)
                      and Research Groups (POF4-511) / TIME-X - TIME
                      parallelisation: for eXascale computing and beyond (955701)},
      pid          = {G:(DE-HGF)POF4-5112 / G:(EU-Grant)955701},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001344332600002},
      doi          = {10.1007/s11075-024-01964-z},
      url          = {https://juser.fz-juelich.de/record/1034860},
}