Multi-grid methods for Hamilton-Jacobi-Bellman equations. (English) Zbl 0577.65088

Hoppe, Ronald H. W.

Numer. Math. 49, 239-254 (1986).

We are concerned with multigrid algorithms for the numerical solution of Hamilton-Jacobi-Bellman equations. The proposed schemes result from a combination of standard multigrid techniques and the iterative methods used by P.-L. Lions and B. Mercier [RAIRO. Anal. Numér. 14, 369-393 (1980; Zbl 0469.65041)]. A convergence result is given and the efficiency of the algorithms is illustrated by some numerical examples.

MSC:

65N22	Numerical solution of discretized equations for boundary value problems involving PDEs
65F10	Iterative numerical methods for linear systems
35L20	Initial-boundary value problems for second-order hyperbolic equations
49L20	Dynamic programming in optimal control and differential games

Keywords:

multigrid methods; Hamilton-Jacobi-Bellman equations; convergence; numerical examples

Citations:

Zbl 0469.65041

References:

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