On the derivation of the modified equation for the analysis of linear numerical methods
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 31 (1997) no. 4, p. 459-470
@article{M2AN_1997__31_4_459_0,
     author = {Carpentier, Romuald and de La Bourdonnaye, Armel and Larrouturou, Bernard},
     title = {On the derivation of the modified equation for the analysis of linear numerical methods},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {31},
     number = {4},
     year = {1997},
     pages = {459-470},
     zbl = {0881.65084},
     mrnumber = {1457456},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1997__31_4_459_0}
}
On the derivation of the modified equation for the analysis of linear numerical methods. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 31 (1997) no. 4, pp. 459-470. http://www.numdam.org/item/M2AN_1997__31_4_459_0/

[1] D. A. Anderson, J. C. Tannehill and R. H. Pletcher, Computational fluid mechanics and heat transfer (Hemisphere, Mc Graw-Hill, 1984). | MR 761171 | Zbl 0569.76001

[2] R. Carpentier, A. De La Bourdonnaye and B. Larrouturou, 1994, On the derivation of the modified equation for the analysis of linear numerical methods, CERMICS Report No 94-26. | MR 1300083

[3] R. Carpentier, 1995, Approximation et analyse numérique d'écoulement instationnaire. Application à des instabilités tourbillonnaires, Thesis, Université de Nice.

[4] S. C. Chang, 1990, A critical analysis of the modified equation technique of Warming and Hyett, J. Comput. Phys., 86, pp. 107-126. | MR 1033903 | Zbl 0689.65059

[5] D. Chargy, 1991, Étude numérique d'écoulements réactifs transsoniques, Thesis, ENPC, Paris.

[6] N. Glinsky, 1990, Simulation numérique d'écoulements hypersoniques réactifs hors-équilibre chimique, Thesis, Université de Nice. | Zbl 0923.76078

[7] J. Goodman and A. Majda, 1985, The validity of the modified equation for nonlinear shock waves, J. Comput. Phys., 58, pp. 336-348. | MR 792414 | Zbl 0581.76072

[8] S. Lanteri, 1991, Simulation d'écoulements aérodynamiques instationnaires sur une architecture SIMD massivement parallèle, Thesis, Université de Nice.

[9] R. Peyret, 1977, Résolution numérique des systèmes hyperboliques. Application à la dynamique des gaz, ONERA Report 1977-5.

[10] M. Spiridonova and J. A. Desideri, Symbolic computations for the analysis of finite-difference schemes by the modified equation approach (unpublished).

[11] Yu. I. Shokin, The Method of Differential Approximation (Springer Verlag, 1983). | MR 704817 | Zbl 0511.65067

[12] R. F. Warming and F. Hyett, 1974, The modified equation approach to the stability and accuracy analysis of finite-difference methods, J. Comput. Phys., 14, 2, p. 159. | MR 339526 | Zbl 0291.65023