Year: 2001
Author: Hua-Zhong Tang, Hua-Mu Wu
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 3 : pp. 231–240
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2001-JCM-8976
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 3 : pp. 231–240
Published online: 2001-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: The relaxing scheme The relaxing systems Hamilton-Jacobi equation Hyperbolic conservation law.