The Viscosity Solution Approach to Proving Convergence of Numerical Schemes

1992 ◽  
pp. 411-421
Author(s):  
Harold J. Kushner ◽  
Paul G. Dupuis
Keyword(s):  
Viscosity Solution ◽  
Numerical Schemes ◽  
Solution Approach

scholarly journals Some non monotone schemes for Hamilton-Jacobi-Bellman equations

2019 ◽  
Vol 65 ◽  
pp. 476-497
Author(s):  
Xavier Warin
Keyword(s):  
Viscosity Solution ◽  
Discrete Problem ◽  
Numerical Schemes ◽  
Bellman Equations ◽  
Monotone Schemes ◽  
Hamilton Jacobi Bellman

We extend the theory of Barles Jakobsen [3] for a class of almost monotone schemes to solve stationary Hamilton Jacobi Bellman equations. We show that the monotonicity of the schemes can be relaxed still leading to the convergence to the viscosity solution of the equation even if the discrete problem can only be solved with some error. We give some examples of such numerical schemes and show that the bounds obtained by the framework developed are not tight. At last we test the schemes.

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