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Adaptive spline interpolation for Hamilton–Jacobi–Bellman equations

Title data

Bauer, Florian ; Grüne, Lars ; Semmler, Willi:
Adaptive spline interpolation for Hamilton–Jacobi–Bellman equations.
In: Applied Numerical Mathematics. Vol. 56 (September 2006) Issue 9 . - pp. 1196-1210.
ISSN 1873-5460
DOI: https://doi.org/10.1016/j.apnum.2006.03.011

Abstract in another language

We study the performace of adaptive spline interpolation in semi--Lagrangian discretization schemes for Hamilton--Jacobi--Bellman equations. We investigate the local approximation properties of cubic splines on locally refined grids by a theoretical analysis. Numerical examples show how this method performs in practice. Using those examples we also illustrate numerical stability issues.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: Special Issue: Numerical Methods for Viscosity Solutions and Applications
Keywords: Viscosity solution; Optimal control; Adaptive discretization; Spline interpolation; Adaptive grids; Fixed point equation; Numerical example; Convergence; Numerical stability
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Result of work at the UBT: Yes
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Date Deposited: 02 Mar 2021 11:17
Last Modified: 23 Mar 2021 09:12
URI: https://eref.uni-bayreuth.de/id/eprint/63586