Stability and convergence of second order backward differentiation schemes for parabolic Hamilton-Jacobi-Bellman equations
Résumé
We study a second order BDF (Backward Differentiation Formula) scheme for the numerical approximation of parabolic HJB (Hamilton-Jacobi-Bellman) equations.
The scheme under consideration is implicit, non-monotone, and second order accurate in time and space.
The lack of monotonicity prevents the use of well-known convergence results for solutions in the viscosity sense.
In this work, we establish rigorous stability results in a general nonlinear setting as well as convergence results for some particular cases with additional regularity assumptions.
While most results are presented for one-dimensional, linear parabolic and non-linear HJB equations, some results are also extended to multiple dimensions and to Isaacs equations.
Numerical tests are included to validate the method.
Domaines
Analyse numérique [math.NA]Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...