Singly Diagonally Implicit Runge–Kutta Methods with an Explicit First Stage. Kværnø, A. BIT Numerical Mathematics, 44(3):489–502, Kluwer Academic Publishers, 2004.
doi  abstract   bibtex   
The purpose of this paper is to construct methods for solving stiff ODEs, in particular singular perturbation problems. We consider embedded pairs of singly diagonally implicit Runge–Kutta methods with an explicit first stage (ESDIRKs). Stiffly accurate pairs of order 3/2, 4/3 and 5/4 are constructed.
@Article{         Kvaerno_2004aa,
  abstract      = {The purpose of this paper is to construct methods for solving stiff ODEs, in particular singular perturbation problems. We consider embedded pairs of singly diagonally implicit Runge--Kutta methods with an explicit first stage (ESDIRKs). Stiffly accurate pairs of order 3/2, 4/3 and 5/4 are constructed.},
  author        = {Kværnø, Anne},
  doi           = {10.1023/B:BITN.0000046811.70614.38},
  file          = {Kvaerno_2004aa.pdf},
  issn          = {0006-3835},
  journal       = {BIT Numerical Mathematics},
  keywords      = {ode,numerics},
  langid        = {english},
  number        = {3},
  pages         = {489--502},
  publisher     = {Kluwer Academic Publishers},
  title         = {Singly Diagonally Implicit {Runge}--{Kutta} Methods with an Explicit First Stage},
  volume        = {44},
  year          = {2004},
  shortjournal  = {BIT}
}
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