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High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations. (English) Zbl 0736.65066
The first author and {\it J. A. Sethian} [J. Comput. Phys. 79, No. 1, 12- 49 (1988; Zbl 0659.65132)] constructed essentially nonoscillatory (ENO) schemes for the Hamilton-Jacobi equation and its perturbations, arising in front propagation problems. In this paper a more general ENO scheme construction procedure is provided mainly by considering different multidimensional monotone building blocks. The schemes are numerically tested on a variety of one- and two-dimensional problems including a problem related to control optimization, checking the accuracy in smooth regions, resolution of discontinuities in derivatives, and the phenomenon of convergence to viscosity solutions.

65M06Finite difference methods (IVP of PDE)
35L45First order hyperbolic systems, initial value problems
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