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@ARTICLE{Akramov:1037643,
      author       = {Akramov, Ikrom and Götschel, Sebastian and Minion, Michael
                      and Ruprecht, Daniel and Speck, Robert},
      title        = {{S}pectral {D}eferred {C}orrection {M}ethods for
                      {S}econd-{O}rder {P}roblems},
      journal      = {SIAM journal on scientific computing},
      volume       = {46},
      number       = {3},
      issn         = {1064-8275},
      address      = {Philadelphia, Pa.},
      publisher    = {SIAM},
      reportid     = {FZJ-2025-00808},
      pages        = {A1690 - A1713},
      year         = {2024},
      abstract     = {Spectral deferred corrections (SDC) are a class of
                      iterative methods for the numerical solution of ordinary
                      differential equations. SDC can be interpreted as a Picard
                      iteration to solve a fully implicit collocation problem,
                      preconditioned with a low-order method. It has been widely
                      studied for first-order problems, using explicit, implicit,
                      or implicit-explicit Euler and other low-order methods as
                      preconditioner. For first-order problems, SDC achieves
                      arbitrary order of accuracy and possesses good stability
                      properties. While numerical results for SDC applied to the
                      second-order Lorentz equations exist, no theoretical results
                      are available for SDC applied to second-order problems. We
                      present an analysis of the convergence and stability
                      properties of SDC using velocity-Verlet as the base method
                      for general second-order initial value problems. Our
                      analysis proves that the order of convergence depends on
                      whether the force in the system depends on the velocity. We
                      also demonstrate that the SDC iteration is stable under
                      certain conditions. Finally, we show that SDC can be
                      computationally more efficient than a simple Picard
                      iteration or a fourth-order Runge–Kutta–Nyström
                      method.},
      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:001293445800002},
      doi          = {10.1137/23M1592596},
      url          = {https://juser.fz-juelich.de/record/1037643},
}