THE RELAXING SCHEMES FOR HAMILTON-JACOBI EQUATIONS

• 来源期刊: 计算数学(英文版)
• 学科: 数学
• 关键词: The relaxing scheme The relaxing systems Hamilton-Jacobi equation Hyperbolic conservation laws.
• 年，卷（期）: 2001,（3）
• 页码范围: 231-240
• 页数: 10页
• 分类号: O1
• 语种: 英文

摘要

Hamilton-Jacobiequation 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 HamiltonJacobiequations 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.