@Article{JCM-19-3,
author = {Tang, Hua-Zhong and Wu, Hua-Mu},
title = {The Relaxing Schemes for Hamilton-Jacobi Equations},
journal = {Journal of Computational Mathematics},
year = {2001},
volume = {19},
number = {3},
pages = {231--240},
abstract = {<p style="text-align: justify;">Hamilton-Jacobi equation appears frequently in applications, e.g., in differential games and control theory, and is closely related to hyperbolic conservation laws[3, 4, 12]. This is helpful in the design of difference approximations for Hamilton-Jacobi equation and hyperbolic conservation laws. In this paper we present the relaxing system for Hamilton-Jacobi equations in arbitrary space dimensions, and high resolution relaxing schemes for Hamilton-Jacobi equation, based on using the local relaxation approximation. The schemes are numerically tested on a variety of 1D and 2D problems, including a problem related to optimal control problem. High-order accuracy in smooth regions, good resolution of discontinuities, and convergence to viscosity solutions are observed.</p>},
issn = {1991-7139},
doi = {https://doi.org/2001-JCM-8976},
url = {https://global-sci.com/article/85469/the-relaxing-schemes-for-hamilton-jacobi-equations}
}