no. 4
On the derivation of the modified equation for the analysis of linear numerical methods
ESAIM: Modélisation mathématique et analyse numérique, Tome 31 (1997) no. 4, pp. 459-470 
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     title = {On the derivation of the modified equation for the analysis of linear numerical methods},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {459--470},
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     zbl = {0881.65084},
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Carpentier, Romuald; de La Bourdonnaye, Armel; Larrouturou, Bernard. On the derivation of the modified equation for the analysis of linear numerical methods. ESAIM: Modélisation mathématique et analyse numérique, Tome 31 (1997) no. 4, pp. 459-470. https://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). | Zbl | MR

[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

[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. | Zbl | MR

[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

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

[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J. A. Desideri, Symbolic computations for the analysis of finite-difference schemes by the modified equation approach (unpublished).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). | Zbl | MR

[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. | Zbl | MR