Approximation of solution branches of nonlinear equations

Jean Descloux; Jacques Rappaz

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1982)

  • Volume: 16, Issue: 4, page 319-349
  • ISSN: 0764-583X

How to cite

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Descloux, Jean, and Rappaz, Jacques. "Approximation of solution branches of nonlinear equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 16.4 (1982): 319-349. <http://eudml.org/doc/193402>.

@article{Descloux1982,
author = {Descloux, Jean, Rappaz, Jacques},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {bifurcating branches; Galerkin methods; Banach spaces; solution branches; bifurcation points; limit points},
language = {eng},
number = {4},
pages = {319-349},
publisher = {Dunod},
title = {Approximation of solution branches of nonlinear equations},
url = {http://eudml.org/doc/193402},
volume = {16},
year = {1982},
}

TY - JOUR
AU - Descloux, Jean
AU - Rappaz, Jacques
TI - Approximation of solution branches of nonlinear equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1982
PB - Dunod
VL - 16
IS - 4
SP - 319
EP - 349
LA - eng
KW - bifurcating branches; Galerkin methods; Banach spaces; solution branches; bifurcation points; limit points
UR - http://eudml.org/doc/193402
ER -

References

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  1. [1] F BREZZI, J APPAZ and P A RAVIART, Finite Dimensional Approximation of Nonlinear Problems, Part I Branches of Nonsingular Solutions, Numer Math 36, 1980, 1-25 Zbl0488.65021MR595803
  2. [2] F BREZZI, J RAPPAZ and P A RAVIART, Finite Dimensional Approximation of Nonlinear Problems, Part II Limit Points, Numer Math , 37, 1981, 1-28. Zbl0525.65036MR615889
  3. [3] F BREZZI, J RAPPAZ and P A RAVIART, Finite Dimensional Approximation of Nonlinear Problems, Part III Simple Bifurcation Points, Numer Math , 38, 1981, 1-30 Zbl0525.65037MR634749
  4. [4] PG CIARLET, The Finite Element Method for Elliptic Problems, Studies in Mathe-matics and its Applications, Vol 4, North-Holland, 1978 Zbl0383.65058MR520174
  5. [5] D W DECKER and H B KELLER, Multiple Limite Point Bifurcation Report of Math Dept, California Institute of Technology, 1979 
  6. [6] J DESCLOUX, M LUSKIN and J RAPPAZ, Approximation of the Spectrum of Closed Operators The Determination of Normal Modes of a Rotating Basin, Math Comp, 36, 1981, 137-154 Zbl0458.65084MR595047
  7. [7] J DESCLOUX, N NASSIE and J RAPPAZ, On Spectral Approximation, RAIRO Numerical Analysis, 191, 137-154 Zbl0393.65024
  8. [8] J DESCLOUX and J RAPPAZ, On Numerical Approximation of Solution Branches of Nonhnear Equations, Rapport, , Departement de Mathématiques, EPFL, 1981 Zbl0505.65016
  9. [9] J DESCLOUX and J RAPPAZ, Numerical Approximation of a Nonlinear Sturm-Liouville Problem on an Infinité Interval, to appear m the Proceedings of Equa-diff V, Teubner Zbl0514.65068
  10. [10] R J MAGNUS, On the Local Structure of the Zero-Set of a Banach Space Valued Mapping , J Functional Analysis, 22, 1976, 58-72 Zbl0321.47042MR418149
  11. [11] J -C PAUMIER, Une methode numérique pour le calcul des points de retournement Application a un problème aux limites non-lineaire II Analyse numérique d'un problème aux limites non-lineaire, Numer Math , 37, 1981, 445-454 Zbl0449.65025MR627116
  12. [11] J RAPPAZ and G RAUGEL, Finite Dimensional Approximation of Bifurcation Problems at a Multiple Eigenvalue, Rapport no 71, Centre de Mathématiques appliquées, Ecole Polytechnique, Palaiseau, 1981 Zbl0571.65048
  13. [13] J RAPPAZ and G RAUGEL, Approximation of Double Bifurcation Points for Nonlinear Eigenvalue Problems, MAFELAP 1981 (Ed J Whiteman), Academic Press (to appear) Zbl0571.65048
  14. [14] D H SATTINGER, Group Theorie Methods in Bifurcation Theory, Lecture Notes in Mathematics 762, Springer-Verlag, Berlin, 1979 Zbl0414.58013

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