On application of an alternating direction method to Hamilton--Jacobin--Bellman equations.

DOI10.1016/j.cam.2003.09.031zbMath1044.65056OpenAlexW1978760430WikidataQ59416208 ScholiaQ59416208MaRDI QIDQ1428495

Songgui Wang, Kok Lay Teo, Chieh-Sen Huang

Publication date: 29 March 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2003.09.031

zbMATH Keywords

Hamilton-Jacobi-Bellman equationnumerical resultssingular perturbationFinite difference methodmethod of characteristicsAlternating direction methodViscosity solutionOptimal feedback control

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Discrete approximations in optimal control (49M25)

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Cites Work

• Numerical solution of Hamilton-Jacobi-Bellman equations by an upwind finite volume method
• Solving Hamilton-Jacobi-Bellman equations by a modified method of characteristics
• A general formulation of alternating direction methods. I: Parabolic and hyperbolic problems
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• On the Numerical Integration of $\frac{\partial ^2 u}{\partial x^2 } + \frac{\partial ^2 u}{\partial y^2 } = \frac{\partial u}{\partial t}$ by Implicit Methods
• Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
• On a new principle of superposition for optimization problems
• Viscosity Solutions of Hamilton-Jacobi Equations
• Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures
• An upwind finite-difference method for the approximation of viscosity solutions to Hamilton-Jacobi-Bellman equations
• IMPROVED ACCURACY FOR LOCALLY ONE-DIMENSIONAL METHODS FOR PARABOLIC EQUATIONS
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
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