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Original Articles

Rosenbrock methods with an explicit first stage

Pages 995-1010 | Received 02 Nov 2013, Accepted 02 Dec 2014, Published online: 27 Mar 2015

References

  • M.H. Carpenter, D. Gottlieb, S. Abarbanel, and W.-S. Don, The theoretical accuracy of Runge–Kutta time discretizations for the initial boundary value problem: a study of the boundary error, SIAM J. Sci. Comput. 16 (1995), pp. 1241–1252. Available at http://link.aip.org/link/?SCE/16/1241/1http://link.aip.org/link/?SCE/16/1241/1. doi: 10.1137/0916072
  • E. Hairer and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer-Verlag, Berlin, Heidelberg, 1993.
  • W. Hundsdorfer and J. Verwer, Numerical Solution of Time-dependent Advection–Diffusion–Reaction Equations, Springer Series in Computational Mathematics, Vol. 33, Springer-Verlag, Berlin, 2003.
  • A. Kværnø, Singly diagonally implicit Runge–Kutta methods with an explicit first stage, BIT Numer. Math. 44 (2004), pp. 489–502. doi: 10.1023/B:BITN.0000046811.70614.38
  • Ch. Lubich and A. Ostermann, Linearly implicit time discretization of non-linear parabolic equations, IMA J. Numer. Math. 15 (1995), pp. 555–583. doi: 10.1093/imanum/15.4.555
  • A. Ostermann and M. Roche, Rosenbrock methods for partial differential equations and fractional orders of convergence, SIAM J. Numer. Anal. 30 (1993), pp. 1084–1098. doi: 10.1137/0730056
  • J.M. Sanz-Serna and J.G. Verwer, Stability and convergence at the PDE/stiff ODE interface, Appl. Numer. Math. 5 (1989), pp. 117–132. doi: 10.1016/0168-9274(89)90028-7
  • J. Sanz-Serna, J. Verwer, and W. Hundsdorfer, Convergence and order reduction of Runge–Kutta schemes applied to evolutionary problems in partial differential equations, Numer. Math. 50 (1987), pp. 405–418. doi: 10.1007/BF01396661

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