@Article{         Clemens_2003aa,
  abstract      = { Linear-implicit time-step methods of the Rosenbrock type are proposed for the time-integration of the nonlinear differential-algebraic systems of equations that arise in transient magnetic field simulations. These methods avoid the iterative solution of the nonlinear systems due to their built-in Newton procedures. Embedded lower order schemes allow an error-controlled adaptive time stepping to take into account the dynamics of the underlying process. Numerical tests show the applicability of these methods for error-controlled adaptive time-integration of nonlinear magnetodynamic problems and the comparison to established singly diagonal implicit Runge-Kutta methods shows the benefits and possible problems of these specialized Runge-Kutta methods.},
  author        = {Clemens, Markus and Wilke, Markus and Weiland, Thomas},
  doi           = {10.1109/TMAG.2003.810221},
  file          = {Clemens_2003aa.pdf},
  issn          = {0018-9464},
  journal       = {IEEE Transactions on Magnetics},
  keywords      = {field,dae,physics,stiffness,nonlinear,numerics,fit,fem},
  langid        = {english},
  month         = may,
  number        = {3},
  pages         = {1175--1178},
  publisher     = {IEEE},
  title         = {Linear-implicit time-integration schemes for error-controlled transient nonlinear magnetic field simulations},
  volume        = {39},
  year          = {2003},
  shortjournal  = {IEEE Trans. Magn.}
}

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