Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations
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- by Guy Barles and Espen R. Jakobsen;
- Math. Comp. 76 (2007), 1861-1893
- DOI: https://doi.org/10.1090/S0025-5718-07-02000-5
- Published electronically: April 20, 2007
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Abstract:
We obtain nonsymmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton-Jacobi-Bellman equations by introducing a new notion of consistency. Our results are robust and general – they improve and extend earlier results by Krylov, Barles, and Jakobsen. We apply our general results to various schemes including Crank–Nicholson type finite difference schemes, splitting methods, and the classical approximation by piecewise constant controls. In the first two cases our results are new, and in the last two cases the results are obtained by a new method which we develop here.References
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Bibliographic Information
- Guy Barles
- Affiliation: Laboratoire de Mathématiques et Physique Théorique, University of Tours, 37200 Tours, France
- Email: barles@lmpt.univ-tours.fr
- Espen R. Jakobsen
- Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
- Email: erj@math.ntnu.no
- Received by editor(s): June 24, 2005
- Received by editor(s) in revised form: June 29, 2006
- Published electronically: April 20, 2007
- Additional Notes: Jakobsen was supported by the Research Council of Norway, grant no. 151608/432
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 76 (2007), 1861-1893
- MSC (2000): Primary 65M15, 65M06, 35K60, 35K70, 49L25
- DOI: https://doi.org/10.1090/S0025-5718-07-02000-5
- MathSciNet review: 2336272