On the derivation of the modified equation for the analysis of linear numerical methods

Romuald Carpentier; Armel de La Bourdonnaye; Bernard Larrouturou

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1997)

  • Volume: 31, Issue: 4, page 459-470
  • ISSN: 0764-583X

How to cite

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Carpentier, Romuald, de La Bourdonnaye, Armel, and Larrouturou, Bernard. "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 31.4 (1997): 459-470. <http://eudml.org/doc/193845>.

@article{Carpentier1997,
author = {Carpentier, Romuald, de La Bourdonnaye, Armel, Larrouturou, Bernard},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {error analysis; evolution equation; modified equation technique},
language = {eng},
number = {4},
pages = {459-470},
publisher = {Dunod},
title = {On the derivation of the modified equation for the analysis of linear numerical methods},
url = {http://eudml.org/doc/193845},
volume = {31},
year = {1997},
}

TY - JOUR
AU - Carpentier, Romuald
AU - de La Bourdonnaye, Armel
AU - Larrouturou, Bernard
TI - On the derivation of the modified equation for the analysis of linear numerical methods
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1997
PB - Dunod
VL - 31
IS - 4
SP - 459
EP - 470
LA - eng
KW - error analysis; evolution equation; modified equation technique
UR - http://eudml.org/doc/193845
ER -

References

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  1. [1] D. A. ANDERSON, J. C. TANNEHILL and R. H. PLETCHER, Computational fluid mechanics and heat transfer (Hemisphere, Mc Graw-Hill, 1984). Zbl0569.76001MR761171
  2. [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. Zbl0806.65089MR1300083
  3. [3] R. CARPENTIER, 1995, Approximation et analyse numérique d'écoulement instationnaire. Application à des instabilités tourbillonnaires, Thesis, Université de Nice. 
  4. [4] S. C. CHANG, 1990, A critical analysis of the modified equation technique of Warming and Hyett, J. Comput. Phys., 86, pp. 107-126. Zbl0689.65059MR1033903
  5. [5] D. CHARGY, 1991, Étude numérique d'écoulements réactifs transsoniques, Thesis, ENPC, Paris. 
  6. [6] N. GLINSKY, 1990, Simulation numérique d'écoulements hypersoniques réactifs hors-équilibre chimique, Thesis, Université de Nice. Zbl0923.76078
  7. [7] J. GOODMAN and A. MAJDA, 1985, The validity of the modified equation for nonlinear shock waves, J. Comput. Phys., 58, pp. 336-348. Zbl0581.76072MR792414
  8. [8] S. LANTERI, 1991, Simulation d'écoulements aérodynamiques instationnaires sur une architecture SIMD massivement parallèle, Thesis, Université de Nice. 
  9. [9] R. PEYRET, 1977, Résolution numérique des systèmes hyperboliques. Application à la dynamique des gaz, ONERA Report 1977-5. 
  10. [10] M. SPIRIDONOVA and J. A. DESIDERI, Symbolic computations for the analysis of finite-difference schemes by the modified equation approach (unpublished). 
  11. [11] Yu. I. SHOKIN, The Method of Differential Approximation (Springer Verlag, 1983). Zbl0511.65067MR704817
  12. [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. Zbl0291.65023MR339526

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