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In this work, we propose a high-resolution alternating evolution (AE) scheme to solve Hamilton–Jacobi equations. The construction of the AE scheme is based on an alternating evolution system of the Hamilton–Jacobi equation, following the idea previously developed for hyperbolic conservation laws. A semidiscrete scheme derives directly from a sampling of… (More)

The alternating evolution (AE) system of Liu [27] ∂tu + ∂xf (v) = 1 (v − u), ∂tv + ∂xf (u) = 1 (u − v), serves as a refined description of systems of hyperbolic conservation laws ∂tφ + ∂xf (φ) = 0, φ(x, 0) = φ 0 (x). The solution of conservation laws is precisely captured when two components take the same initial value as φ 0 , or approached by two… (More)

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