Adaptive spline interpolation for Hamilton-Jacobi-Bellman equations

Authors:
Florian Bauer;Lars Grüne;Willi Semmler
Affiliations:
Mathematisches Institut, Universität Bayreuth, Bayreuth, Germany;Mathematisches Institut, Universität Bayreuth, Bayreuth, Germany;Center for Empirical Macroeconomics, Bielefeld and New School University, New York
Venue:
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
Year:
2006

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Abstract

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.