Convergence of numerical algorithms for semilinear hyperbolic system

D. Aregba-Driollet; J.-M. Mercier

Rendiconti del Seminario Matematico della Università di Padova (1999)

  • Volume: 102, page 241-283
  • ISSN: 0041-8994

How to cite

top

Aregba-Driollet, D., and Mercier, J.-M.. "Convergence of numerical algorithms for semilinear hyperbolic system." Rendiconti del Seminario Matematico della Università di Padova 102 (1999): 241-283. <http://eudml.org/doc/108505>.

@article{Aregba1999,
author = {Aregba-Driollet, D., Mercier, J.-M.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {semilinear hyperbolic systems; explicit finite difference scheme; stability; consistency; convergence; systems of wave equations; numerical experiments; Broadwell system},
language = {eng},
pages = {241-283},
publisher = {Seminario Matematico of the University of Padua},
title = {Convergence of numerical algorithms for semilinear hyperbolic system},
url = {http://eudml.org/doc/108505},
volume = {102},
year = {1999},
}

TY - JOUR
AU - Aregba-Driollet, D.
AU - Mercier, J.-M.
TI - Convergence of numerical algorithms for semilinear hyperbolic system
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1999
PB - Seminario Matematico of the University of Padua
VL - 102
SP - 241
EP - 283
LA - eng
KW - semilinear hyperbolic systems; explicit finite difference scheme; stability; consistency; convergence; systems of wave equations; numerical experiments; Broadwell system
UR - http://eudml.org/doc/108505
ER -

References

top
  1. [1] D. Aregba-Driollet, The blow up curve for a semilinear hyperbolic system, preprint 95008 Mathématiques Appliquées de Bordeaux (1995). 
  2. [2] D. Aregba-Driollet - B. Hanouzet, Cauchy problem for one-dimensional semilinear hyperbolic systems: global existence, blow up, J. Differential Equations, 125 (1996), pp. 1-26. Zbl0859.35069MR1376058
  3. [3] J.M. Bony, Existence globale à données de pour les modèles discrets de l'équation de Boltzmann, Comm. in partial differential equations, 16 (1991). Zbl0736.35064MR1113097
  4. [4] L.A. Caffarelli - A. FRIEDMAN, The blow-up boundary for nonlinear wave equations, Trans. Amer. Math. Soc., 297 (1986), pp. 223-241. Zbl0638.35053MR849476
  5. [5] R.E. Caflisch - S. Jin - G. Russo, Uniformly accurate schemes for hyperbolic systems with relaxation. Technical report, Università dell'Aquila (1994). Zbl0868.35070
  6. [6] F. Castillo-Aranguren - H. Juarez-Valencia - A. Nicolas-Carrizosa, Theoritical and numerical aspects of some semilinear hyperbolic problems, Calcolo (1994), pp. 337-354. Zbl0815.35068MR1353273
  7. [7] A.J. Chorin - T. Jr. Hugues - M.F. McCracken - J.E. Marsden, Product formulas and numerical algorithms, CPAM, 31 (1978), p. 205-256. Zbl0358.65082MR488713
  8. [8] D. Driollet - B. Hanouzet, Systèmes hyperboliques semi-linéaires conservatifs 1-d, C.R. Acad. Sc. Paris, 307, serie I (1988), pp. 231-234. Zbl0696.35102MR956812
  9. [9] E. Gabetta - L. Pareschi, Approximating the Broadwell model in a strip, Math. Models and Methods in Appl. Sci., 2 (1992), pp. 1-19. Zbl0763.76070MR1159473
  10. [10] T. Kato, Nonlinear equations of evolution in banach spaces, Proc. Sympos. Pure Math., 45 (2) (1986), pp. 9-23. Zbl0606.35049MR843591
  11. [11] D.J. Kaup - A. REIMAN - A. BERS, Space-time evolution of nonlinear three-wave interaction. 1. interaction in a homogeneous medium, Reviews of Modern Physics, 51 (1979). MR536598
  12. [12] A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Springer Verlag, New York (1984). Zbl0537.76001MR748308
  13. [13] J.-M. Mercier, Sur des Systèmes d'équations des ondes semi-linéaires. PhD thesis, université Bordeaux, 1 (1996). 
  14. [14] J.-M. Mercier, Global existence and long time estimation for an integrodifferential system, Preprint dell' universita di Pisa 2.275.1047, to be published in Ricerche di Matematica (1997). Zbl0955.45008
  15. [15] J.M. Mercier, Note over a multigrid adaptive mesh refinement technique for hyperbolic problems, preprint SISSA 53/98/M (1998). 
  16. [16] R. Natalini - B. RUBINO, A discrete approximation for hyperbolic systems with quadratic interaction term, Comm. Appl. Nonlinear Anal., 3 (1996), pp. 1-21. Zbl0874.35066MR1379435
  17. [17] Kuo Pen-Yu - L. Vasquez, Numerical solution of a nonlinear wave equation in polar coordinates, Appl. Math. Comput., 14 (1984), pp. 313-329. Zbl0542.65068MR744581
  18. [18] W.-A. Strauss - L. Vasquez, Numerical solution of a non-linear equation, J. Comput. Phys., 28 (1978), pp. 271-278. Zbl0387.65076MR503140
  19. [19] L. Tartar, Some existence theorems for semilinear hyperbolic systems in one space variable, Technical Report 2164, University of Wisconsin-Madison (1981). 
  20. [20] R. Temam, Sur la résolution exacte et approchée d'un problème hyperbolique non-linéaire de T. Carleman, Arch. Rational Mech. Anal., 35 (1969), pp. 351-362. Zbl0189.10504MR251376

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.