Essai de résolution numérique du problème de Goursat par la méthode de Runge-Kutta pour une équation aux dérivées partielles du type hyperbolique

André Metté

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1967)

  • Volume: 1, Issue: 1, page 67-90
  • ISSN: 0764-583X

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Metté, André. "Essai de résolution numérique du problème de Goursat par la méthode de Runge-Kutta pour une équation aux dérivées partielles du type hyperbolique." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 1.1 (1967): 67-90. <http://eudml.org/doc/193078>.

@article{Metté1967,
author = {Metté, André},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {numerical analysis},
language = {fre},
number = {1},
pages = {67-90},
publisher = {Dunod},
title = {Essai de résolution numérique du problème de Goursat par la méthode de Runge-Kutta pour une équation aux dérivées partielles du type hyperbolique},
url = {http://eudml.org/doc/193078},
volume = {1},
year = {1967},
}

TY - JOUR
AU - Metté, André
TI - Essai de résolution numérique du problème de Goursat par la méthode de Runge-Kutta pour une équation aux dérivées partielles du type hyperbolique
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1967
PB - Dunod
VL - 1
IS - 1
SP - 67
EP - 90
LA - fre
KW - numerical analysis
UR - http://eudml.org/doc/193078
ER -

References

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  2. [2] A. K. Aziz and B. E. HUBBARD, Bounds on the Truncation error by Finite Difference for the Goursat Problem (Mathematics of computation , Jan. 1964, Vol. 18, n° 85, p. 19). Zbl0141.33003MR160337
  3. [3] BUCHANAN, A necessary and sufficient condition for stability of difference schemes for initial values problems (J. Soc. Indust. Appl. Math., 11, 1963, p. 919-935]. Zbl0221.65144MR160324
  4. [4] J. CONLAN, The Cauchy Problem and the mixed Boundary Value Problem for a non-Linear Hyperbolic Partial Differential equation in two independant variables (Archive for Rational mechanics and Analysis, Vol. 3, n° 4, 1959). Zbl0093.31203MR107092
  5. [5] J. B. DIAZ, On the analogue of the Euler-Cauchy Polygon method for the numerical solution of u x y = f ( x , y , u , u x , u y ) (Archive for Rational mechanics and Analysis, Vol. 1, n° 4, 1958, p. 357). Zbl0084.11501MR104041
  6. [6] G. W. HEDSTROM, The near stability of the Lax-Wendroff method (Numerische Mathematics, Band 7, Heft 1, 1965, p. 73),. Zbl0131.34301MR174182
  7. [7] KREISS, Uber die Stabilitatsdefinition für Differenzengleichungen approximieren (BIT, 1962, p. 153-181). Zbl0109.34702
  8. [8] R. H. MOORE, On approximate Solutions of non Linear Hyperbolic Partial differential equations (Archive for Rational Mechanics and Analysis, Vol. 6, n° 1, 1960, p. 75). Zbl0099.33604MR114998
  9. [9] R. H. MOORE, A Runge-Kutta Procedure for the Goursatt Problem in hyperbolic partial differential equations (Archive for Rational mechanics and analysis, Vol. 7, n° 1, 1961, p. 37). Zbl0097.12004MR120772
  10. [10] K. W. MORTON and S. SCHECHTER, On the stability of finite difference matrices (S.I.A.M. Series B, Vol. 1, 1965, pp. 119-128). Zbl0133.38101MR182170
  11. [11] G. STRANG, Acurate partial differential methods II non linear problems (Numerische mathematik, Band 6, Heft 1, 1964, p. 49). Zbl0143.38204
  12. [12] W. TORNING, Zur numerischen Behandlung von Arfangsinertproblem partieller hyperbolischer Differentialgleichungen zweiter ordnung in zwei unabhangigen Veraderbichen. I. Das Charakterische arfangsirertprobleme (Archive for Rational Mechanics and analysis, Vol. 4, n° 5, 1960, p. 428). Zbl0090.34301
  13. [13] W. TORNIG, Zur numerischen Behandlung von arfangsirertproblemer partiellen hyperbolischer Differential gleichungen zweiter ordnung in zwei unabhangigen Veranderbichen II Das Cauchy Problem (Archive for Rational mechanics and analysis, vol. 4, n° 5, 1960, p. 446). Zbl0090.34301MR129559
  14. [14] VIDAR THOMEE, Stability in the maximum norm (Journal of differential equations, vol. 1, n° 3, 1965, p. 273). , Zbl0259.65086MR176240
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  16. [16] HANS J. STETTER, Stability of non linear Discretization algorithms (numerical Solution of Partial Differential Equations. Edited by James H. Bramble, Academic Press 1966). Zbl0149.11603MR205495

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