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Fast sweeping algorithms for a class of Hamilton-Jacobi equations. (English) Zbl 1049.35020
A new numerical algorithm is derived for strictly convex, homogeneous Hamilton-Jacobi equations including the Hamiltonian \(H(p,q)=\sqrt{ap^2+bq^2-2cpq}\), \(c^2<ab\). A numerical flux of Godunov-type is coupled with a Gauss-Seidel-type of iteration to result in fast algorithms applicable to a class of Hamilton-Jacobi equations for which the fast marching methods would not be of any use. Numerical experiments indicate convergence in a few steps even in rather difficult cases.

MSC:
35A35 Theoretical approximation in context of PDEs
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
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