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To cite this version:M. Sermange. Mathematical and numerical aspects of one-dimensional laminar flame simulation. RR-0446, INRIA. 1985.

Communicated by Roger TemamR6sum6. Une nouvelle m6thode qui g6n6ralise l'algorithme standard des approximations successives est d6velopp6e en vue de d6terminer les points fixes (x*) d'op6rateurs qui admettent une d6riv6e de Fr6chet (A) en x* (seulement) telle que A-I soit injectif. Cette m&hode peut &re appliqu6e en particulier au calcul des solutions de probl6mes non lin6aires au-del~ d'un point de bifurcation, ce qui fait l'objet de la premiere partie. On explicite ensuite dans la deuxi~me partie l'application de cette m6thode ~ un probl6me/~ frontibre libre intervenant en physique des plasmas.Abstract. A new method extending the standard successive approximation algorithm is developed for the determination of fixed points (x*) of operators having a Frechet-derivative (A) at x* (but not everywhere) such that A-1 is injective. This method can specially be applied to compute solutions of nonlinear problems past a point of bifurcation (first part). The application of this method to a free boundary value problem arising in plasma physics is then given in a second part.

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