[Une méthode numérique de résolution de l'equation de Monge–Ampère]
Nous résolvons numériquement l'équation de Monge–Ampère avec donnée au bord périodique en utilisant un algorithme de Newton. Nous prouvons la convergence de l'algorithme, et présentons quelques exemples numériques, pour lesquels une bonne approximation de la solution est obtenue en 10 itérations.
We solve numerically the Monge–Ampère equation with periodic boundary condition using a Newton's algorithm. We prove convergence of the algorithm, and present some numerical examples, for which a good approximation is obtained in 10 iterations.
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@article{CRMATH_2005__340_4_319_0,
author = {Loeper, Gr\'egoire and Rapetti, Francesca},
title = {Numerical solution of the {Monge{\textendash}Amp\`ere} equation by a {Newton's} algorithm},
journal = {Comptes Rendus. Math\'ematique},
pages = {319--324},
publisher = {Elsevier},
volume = {340},
number = {4},
year = {2005},
doi = {10.1016/j.crma.2004.12.018},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.12.018/}
}
TY - JOUR AU - Loeper, Grégoire AU - Rapetti, Francesca TI - Numerical solution of the Monge–Ampère equation by a Newton's algorithm JO - Comptes Rendus. Mathématique PY - 2005 SP - 319 EP - 324 VL - 340 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.12.018/ DO - 10.1016/j.crma.2004.12.018 LA - en ID - CRMATH_2005__340_4_319_0 ER -
%0 Journal Article %A Loeper, Grégoire %A Rapetti, Francesca %T Numerical solution of the Monge–Ampère equation by a Newton's algorithm %J Comptes Rendus. Mathématique %D 2005 %P 319-324 %V 340 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.12.018/ %R 10.1016/j.crma.2004.12.018 %G en %F CRMATH_2005__340_4_319_0
Loeper, Grégoire; Rapetti, Francesca. Numerical solution of the Monge–Ampère equation by a Newton's algorithm. Comptes Rendus. Mathématique, Tome 340 (2005) no. 4, pp. 319-324. doi : 10.1016/j.crma.2004.12.018. http://www.numdam.org/articles/10.1016/j.crma.2004.12.018/
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