no. 2
Solving the systems of equations arising in the discretization of some nonlinear P.D.E.'s by implicit Runge-Kutta methods
ESAIM: Modélisation mathématique et analyse numérique, Tome 31 (1997) no. 2, pp. 251-287. 
@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: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {251--287},
     publisher = {Elsevier},
     volume = {31},
     number = {2},
     year = {1997},
     mrnumber = {1437122},
     zbl = {0869.65060},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1997__31_2_251_0/}
}
TY  - JOUR
AU  - Akrivis, Georgios
AU  - Dougalis, Vassilios A.
AU  - Karakashian, Ohannes
TI  - Solving the systems of equations arising in the discretization of some nonlinear P.D.E.'s by implicit Runge-Kutta methods
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1997
SP  - 251
EP  - 287
VL  - 31
IS  - 2
PB  - Elsevier
UR  - http://www.numdam.org/item/M2AN_1997__31_2_251_0/
LA  - en
ID  - M2AN_1997__31_2_251_0
ER  - 
%0 Journal Article
%A Akrivis, Georgios
%A Dougalis, Vassilios A.
%A Karakashian, Ohannes
%T Solving the systems of equations arising in the discretization of some nonlinear P.D.E.'s by implicit Runge-Kutta methods
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1997
%P 251-287
%V 31
%N 2
%I Elsevier
%U http://www.numdam.org/item/M2AN_1997__31_2_251_0/
%G en
%F 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: Modélisation mathématique et analyse numérique, Tome 31 (1997) no. 2, pp. 251-287. http://www.numdam.org/item/M2AN_1997__31_2_251_0/

[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. | MR | Zbl

[2] R. Alexander, 1991, The modified Newton method in the solution of stiff ordinary differential equations, Math. Comp., 57, pp. 673-701. | MR | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[6] J. C. Butcher, 1987, The numerical analysis of ordinary differerential equations. Runge-Kutta and general linear methods, John Wiley & Sons. | MR | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl