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or perhaps with a forcing term g(u, x, t) on the right-hand side. Here u ϭ In this paper, we further analyze, test, modify, and improve the high order WENO (weighted essentially non-oscillatory) finite differ-and t Ͼ 0.that WENO schemes constructed from the rth order (in L 1 norm) oscillatory) schemes, which were first introduced by ENO schemes are (r ϩ… (More)

In this paper, we present a weighted ENO (essentially non-oscillatory) scheme to approximate the viscosity solution of the Hamilton-Jacobi equation: = 0: This weighted ENO scheme is constructed upon and has the same stencil nodes as the 3 rd order ENO scheme but can be as high as 5 th order accurate in the smooth part of the solution. In addition to the… (More)

We construct, analyze, and implement a new nonoscillatory high-resolution scheme for two-dimensional hyperbolic conservation laws. The scheme is a predictor-corrector method which consists of two steps: starting with given cell averages, we first predict pointvalues which are based on nonoscillatory piecewise-linear reconstructions from the given cell… (More)

In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially non-oscillatory) nite diierence schemes of Liu, Osher and Chan 9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L 1 norm) ENO schemes are (r +1) th order accurate. We propose a new way of measuring the smoothness of a… (More)

Numerical simulations often provide strong evidences for the existence and stability of discrete shocks for certain nite diierence schemes approximating conservation laws. This paper presents a framework for converting such numerical observations to mathematical proofs. The framework is applicable to conservative schemes approximating stationary shocks of… (More)

In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially non-oscillatory) nite dierence schemes of Liu, Osher and Chan [9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L 1 norm) ENO schemes are (r+1) th order accurate. We propose a new way o f measuring the smoothness of a… (More)

focus to solutions and stability. On average, schemes wanted a 93% chance of members getting their Equal focus on solutions and implementation theory into reality scheme to create a strong governance structure to keep on top. from a much larger three-year study focused on the 1996 implementation of Problem How do children's perceptions of structural… (More)

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