@article{M2AN_1997__31_2_251_0,
author = {Akrivis, Georgios and Dougalis, Vassilios A. and Karakashian, Ohannes},
title = {Solving the systems of equations arising in the discretization of some nonlinear P.D.E.'s by implicit Runge-Kutta methods},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {31},
year = {1997},
pages = {251-287},
mrnumber = {1437122},
zbl = {0869.65060},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_1997__31_2_251_0}
}
Akrivis, Georgios; Dougalis, Vassilios A.; Karakashian, Ohannes. Solving the systems of equations arising in the discretization of some nonlinear P.D.E.'s by implicit Runge-Kutta methods. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 31 (1997) pp. 251-287. http://gdmltest.u-ga.fr/item/M2AN_1997__31_2_251_0/
[1] , and , 1991, On fully discrete Galerkin methods of second-order temporal accuracy for the Nonlinear Schrödinger Equation, Numer. Math., 59, pp. 31-53. | MR 1103752 | Zbl 0739.65096
[2] , 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] , and , 1983, Convergence of Galerkin approximations for the Korteweg-de Vries equation, Math. Comp., 40, pp. 419-433. | MR 689464 | Zbl 0519.65073
[4] , , and , 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] and , 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] , 1987, The numerical analysis of ordinary differerential equations. Runge-Kutta and general linear methods, John Wiley & Sons. | MR 878564 | Zbl 0616.65072
[7] , and , 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] and , 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] and , 1991, Solving ordinary differential equations II. Stiff and differential-algebraic problems, Springer series in Computational Mathematics, Springer Verlag. | MR 1111480 | Zbl 0729.65051
[10] and , 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] , and , 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] and , 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] and , 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] and , 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