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Article Dans Une Revue Numerische Mathematik Année : 2021

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.
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Dates et versions

hal-01628040 , version 1 (02-11-2017)
hal-01628040 , version 2 (22-02-2018)

Identifiants

Citer

Olivier Bokanowski, Athena Picarelli, Christoph Reisinger. Stability and convergence of second order backward differentiation schemes for parabolic Hamilton-Jacobi-Bellman equations. Numerische Mathematik, 2021, 148 (1), pp.187-222. ⟨10.1007/s00211-021-01202-x⟩. ⟨hal-01628040v2⟩
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