Free Access
Issue
ESAIM: M2AN
Volume 31, Number 2, 1997
Page(s) 251 - 287
DOI https://doi.org/10.1051/m2an/1997310202511
Published online 31 January 2017
  1. G. D. AKRIVIS, V. A. DOUGALIS and O. A. KARAKASHIAN, 1991, On fully discrete Galerkin methods of second-order temporal accuracy for the Nonlinear Schrödinger Equation, Numer. Math., 59, pp. 31-53. [EuDML: 133538] [MR: 1103752] [Zbl: 0739.65096]
  2. R. ALEXANDER, 1991, The modified Newton method in the solution of stiff ordinary differential equations, Math. Comp., 57, pp. 673-701. [MR: 1094939] [Zbl: 0734.65060]
  3. G. A. BAKER, V. A. DOUGALIS and O. A. KARAKASHIAN, 1983, Convergence of Galerkin approximations for the Korteweg-de Vries equation, Math. Comp., 40, pp. 419-433. [MR: 689464] [Zbl: 0519.65073]
  4. J. L. BONA, V. A. DOUGALIS, O. A. KARAKASHIAN and W. R. McKlNNEY, 1995, Conservative high order numerical methods for the generalized Korteweg-de Vries equation, Phil. Trans. Roy. Soc. London Ser. A, 351, pp. 107-164. [MR: 1336983] [Zbl: 0824.65095]
  5. J. L. BONA and R. SMITH, 1975, The initial value problem for the Korteweg-de Vries equation, Philos. Trans. Roy. Soc. London Ser. A, 298, pp. 555-604. [MR: 385355] [Zbl: 0306.35027]
  6. J. C. BUTCHER, 1987, The numerical analysis of ordinary differerential equations. Runge-Kutta and general linear methods, John Wiley & Sons. [MR: 878564] [Zbl: 0616.65072]
  7. M. CROUZEIX, W. H. HUNDSDORFER and M. N. SPIJKER, 1983, On the existence of solutions to the algebraic equations in implicit Runge-Kutta methods, BIT, 23, pp. 84-91. [MR: 689606] [Zbl: 0506.65030]
  8. V. A. DOUGALIS and O. A. KARAKASHIAN, 1985, On some high order accurate fully discrete Galerkin methods for the Korteweg-de Vries equation, Math. Comp., 45, pp. 329-345. [MR: 804927] [Zbl: 0609.65064]
  9. E. HAIRER and G. WANNER, 1991, Solving ordinary differential equations II. Stiff and differential-algebraic problems, Springer series in Computational Mathematics, Springer Verlag. [MR: 1111480] [Zbl: 0729.65051]
  10. O. KARAKASHIAN and W. RUST, 1988, On the parallel implementation of implicit Runge-Kuta methods, SIAM J. Sci. Sta. Comput., 9, pp. 1085-1090. [MR: 963856] [Zbl: 0664.65068]
  11. O. KARAKASHIAN, G. D. AKRIVIS and V. A. DOUGALIS, 1993, On optimal-order error estimates for the Nonlinear Schrödinger Equation, SIAM J. Numer. Anal., 30, pp. 377-400. [MR: 1211396] [Zbl: 0774.65091]
  12. O. KARAKASHIAN and W. MCKINNEY, 1990, On optimal high order in time approximations for the Korteweg-de Vries equation, Math. Comp., 55, pp. 473-496. [MR: 1035935] [Zbl: 0725.65107]
  13. J. M. SANZ-SERNA and D. F. GRIFFITHS, 1991, A new class of results for the algebraic equations of implicit Runge-Kutta processes, IMA Journal of Numerical Analysis, 11, pp. 449-455. [MR: 1135198] [Zbl: 0738.65067]
  14. V. THOMÉE and B. WENDROFF, 1974, Convergence estimates for Galerkin methods for variable coefficient initial value problems, SIAM J. Numer. Anal., 11, pp. 1059-1068. [MR: 371088] [Zbl: 0292.65052]

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