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@ARTICLE{MartnVaquero:860700,
      author       = {Martín-Vaquero, J. and Kleefeld, Andreas},
      title        = {{ESERK}5: {A} fifth-order extrapolated stabilized explicit
                      {R}unge–{K}utta method},
      journal      = {Journal of computational and applied mathematics},
      volume       = {356},
      issn         = {0377-0427},
      address      = {Amsterdam},
      publisher    = {North-Holland},
      reportid     = {FZJ-2019-01365},
      pages        = {22-36},
      year         = {2019},
      abstract     = {A new algorithm is developed and analyzed for
                      multi-dimensional non-linear parabolic partial differential
                      equations (PDEs) which are semi-discretized in the spatial
                      variables leading to a system of ordinary differential
                      equations (ODEs). It is based on fifth-order extrapolated
                      stabilized explicit Runge–Kutta schemes (ESERK). They are
                      explicit methods, and therefore it is not necessary to
                      employ complicated software for linear or non-linear system
                      of equations. Additionally, they have extended stability
                      regions along the negative real semi-axis, hence they can be
                      considered to solve stiff problems coming from very common
                      diffusion or reaction–diffusion problems.Previously, only
                      lower-order codes (up to fourth-order) have been constructed
                      and made available in the scientific literature. However, at
                      the same time, higher-order codes were demonstrated to be
                      very efficient to solve equations where it is necessary to
                      have a high precision or they have transient zones that are
                      very severe, and where functions change very fast. The new
                      schemes allow changing the step length very easily and with
                      a very small computational cost. Thus, a variable step
                      length, with variable number of stages algorithm is
                      constructed and compared with good numerical results in
                      relation to other well-known ODE solvers.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511)},
      pid          = {G:(DE-HGF)POF3-511},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000463693100002},
      doi          = {10.1016/j.cam.2019.01.040},
      url          = {https://juser.fz-juelich.de/record/860700},
}