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Volume 19, Issue 3
The Relaxing Schemes for Hamilton-Jacobi Equations

Hua-Zhong Tang & Hua-Mu Wu

J. Comp. Math., 19 (2001), pp. 231-240.

Published online: 2001-06

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  • 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.

  • Keywords

The relaxing scheme, The relaxing systems, Hamilton-Jacobi equation, Hyperbolic conservation law.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-19-231, 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 = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8976.html} }
TY - JOUR T1 - The Relaxing Schemes for Hamilton-Jacobi Equations AU - Tang , Hua-Zhong AU - Wu , Hua-Mu JO - Journal of Computational Mathematics VL - 3 SP - 231 EP - 240 PY - 2001 DA - 2001/06 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8976.html KW - The relaxing scheme, The relaxing systems, Hamilton-Jacobi equation, Hyperbolic conservation law. AB -

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.

Tang , Hua-Zhong and Wu , Hua-Mu. (2001). The Relaxing Schemes for Hamilton-Jacobi Equations. Journal of Computational Mathematics. 19 (3). 231-240. doi:
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