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High order variational numerical schemes with application to Nash -MFG vaccination games

Laguzet, Laetitia (2018), High order variational numerical schemes with application to Nash -MFG vaccination games, Ricerche di Matematica, 67, 1, p. 247-269. 10.1007/s11587-018-0366-z

Type
Article accepté pour publication ou publié
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https://hal.archives-ouvertes.fr/hal-01404619
Date
2018
Nom de la revue
Ricerche di Matematica
Volume
67
Numéro
1
Éditeur
Springer
Pages
247-269
Identifiant publication
Métadonnées
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Auteur(s)
Laguzet, Laetitia
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Résumé (EN)
This paper introduces high-order explicit Runge-Kutta numerical schemes in metric spaces. We show that our approach reduces to corresponding Runge-Kutta schemes if the ambient space is Hilbert. We apply these schemes to compute the Nash equilibrium in a Mean Field vaccination Game. Numerical simulations show improvement in the speed of convergence towards the Nash equilibrium; the numerical scheme has high order (two to four) in time.
Mots-clés
Variational scheme; Mean Field Games; Nash equilibrium; Vaccination games; SIR model