×

zbMATH — the first resource for mathematics

Error bounds for monotone approximation schemes for Hamilton-Jacobi-Bellman equations. (English) Zbl 1092.65077
The paper is a continuation of a work by the authors [M2AN Math. Model. Numer. Anal. 36, 33–54 (2002; Zbl 0998.65067)]. It contains error bounds for monotone approximation schemes of Hamilton-Jacobi-Bellman equations. These bounds improve previous results of N. V. Krylov [St. Petersbg. Math. J. 9, No. 3, 639–650 (1998) and Algebra Anal. 9, No. 3, 245–256 (1997; Zbl 0902.65035), Probab. Theory Relat. Fields 117, No. 1, 1–16 (2000; Zbl 0971.65081)] and the authors (loc. cit.). The key step in the proof of these new estimates is the introduction of a switching system which allows the construction of approximate, (almost) smooth supersolutions for the Hamilton-Jacobi-Bellman equation.

MSC:
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35L70 Second-order nonlinear hyperbolic equations
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI