@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] 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
, and , 1991,[2] The modified Newton method in the solution of stiff ordinary differential equations, Math. Comp., 57, pp. 673-701. | MR 1094939 | Zbl 0734.65060
, 1991,[3] Convergence of Galerkin approximations for the Korteweg-de Vries equation, Math. Comp., 40, pp. 419-433. | MR 689464 | Zbl 0519.65073
, and , 1983,[4] 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
, , and , 1995,[5] 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
and , 1975,[6] The numerical analysis of ordinary differerential equations. Runge-Kutta and general linear methods, John Wiley & Sons. | MR 878564 | Zbl 0616.65072
, 1987,[7] On the existence of solutions to the algebraic equations in implicit Runge-Kutta methods, BIT, 23, pp. 84-91. | MR 689606 | Zbl 0506.65030
, and , 1983,[8] 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
and , 1985,[9] Solving ordinary differential equations II. Stiff and differential-algebraic problems, Springer series in Computational Mathematics, Springer Verlag. | MR 1111480 | Zbl 0729.65051
and , 1991,[10] On the parallel implementation of implicit Runge-Kuta methods, SIAM J. Sci. Sta. Comput., 9, pp. 1085-1090. | MR 963856 | Zbl 0664.65068
and , 1988,[11] On optimal-order error estimates for the Nonlinear Schrödinger Equation, SIAM J. Numer. Anal., 30, pp. 377-400. | MR 1211396 | Zbl 0774.65091
, and , 1993,[12] On optimal high order in time approximations for the Korteweg-de Vries equation, Math. Comp., 55, pp. 473-496. | MR 1035935 | Zbl 0725.65107
and , 1990,[13] 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
and , 1991,[14] Convergence estimates for Galerkin methods for variable coefficient initial value problems, SIAM J. Numer. Anal., 11, pp. 1059-1068. | MR 371088 | Zbl 0292.65052
and , 1974,