Stability and convergence of second order backward differentiation schemes for parabolic Hamilton-Jacobi-Bellman equations
Abstract
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.
Keywords
Cite
@article{arxiv.1802.07146,
title = {Stability and convergence of second order backward differentiation schemes for parabolic Hamilton-Jacobi-Bellman equations},
author = {Olivier Bokanowski and Athena Picarelli and Christoph Reisinger},
journal= {arXiv preprint arXiv:1802.07146},
year = {2018}
}