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arXiv · 1802.07146

Stability and convergence of second order backward differentiation schemes for parabolic Hamilton-Jacobi-Bellman equations

Olivier Bokanowski·Athena Picarelli·Christoph Reisinger
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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.

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Olivier Bokanowski, Athena Picarelli, Christoph Reisinger. 2018-02-20. Stability and convergence of second order backward differentiation schemes for parabolic Hamilton-Jacobi-Bellman equations. https://arxiv.org/abs/1802.07146

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