We consider approximation schemes for monotone systems of fully nonlinear second order partial differential equations. We first prove a general convergence result for monotone, consistent and regular schemes. This result is a generalization to the well known framework of Barles-Souganidis, in the case of scalar nonlinear equation. Our second main result provides the convergence rate of approximation schemes for weakly coupled systems of Hamilton-Jacobi- Bellman equations. Examples including finite difference schemes and Semi-Lagrangian schemes are discussed.
Approximation schemes for monotone systems of nonlinear second order partial differential equations: convergence result and error estimate / Ariela, Briani; Camilli, Fabio; Hasnaa, Zidani. - In: DIFFERENTIAL EQUATIONS & APPLICATIONS. - ISSN 1847-120X. - STAMPA. - 4:2(2012), pp. 297-317. [10.7153/dea-04-18]
Approximation schemes for monotone systems of nonlinear second order partial differential equations: convergence result and error estimate
CAMILLI, FABIO;
2012
Abstract
We consider approximation schemes for monotone systems of fully nonlinear second order partial differential equations. We first prove a general convergence result for monotone, consistent and regular schemes. This result is a generalization to the well known framework of Barles-Souganidis, in the case of scalar nonlinear equation. Our second main result provides the convergence rate of approximation schemes for weakly coupled systems of Hamilton-Jacobi- Bellman equations. Examples including finite difference schemes and Semi-Lagrangian schemes are discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.