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Ordered upwind methods for static Hamilton–Jacobi equations: Theory and algorithms. (English) Zbl 1040.65088
The authors develop fast methods for approximating the solutions to a wide class of static Hamilton-Jacobi equations. Numerical solutions of these problems are typically obtained by solving large systems of coupled non-linear discretized equations. Theorems and examples are presented for a theoretical foundation and experimentation of the proposed techniques. An extension of the method is also proposed. It is an illustrative paper to read.

MSC:
65N06 Finite difference methods for boundary value problems involving PDEs
49L20 Dynamic programming in optimal control and differential games
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
49N90 Applications of optimal control and differential games
35F30 Boundary value problems for nonlinear first-order PDEs
35B37 PDE in connection with control problems (MSC2000)
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35L60 First-order nonlinear hyperbolic equations
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