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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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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

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