一类求解Hamilton-Jacobi方程的交错网格差分格式

A Class of Difference Schemes with Staggered Grids for Hamilton-Jacobi Equation

Hamilton- Jacobi方程在控制论和微分对策中有广泛的应用 ,由于其表达形式与双曲守恒律方程极为相近 ,这有利于借助于求解双曲守恒律方程的差分格式来构造求解 Hamilton- Jacobi方程的差分格式。文中将 Ham ilton- Jacobi方程变化为双曲守恒律方程 ,利用求解双曲守恒律方程的交错网格的 Gauss型差分格式 ,构造了一类求解 Hamilton- Jacobi方程的交错网格的 Gauss型差分格式。这类格式具有高分辨、计算简便等优点。最后针对一系列的一维和二维问题进行了数值试验 ,试验结果很令人满意。

Hamilton Jacobi (HJ) equations are frequently encountered in applications, e.g., in differential games and control theory, they are closely related to hyperbolic conservation laws. It is helpful for us to construct difference approximation schemes for HJ equation with aids of schemes for conservation laws. This paper presents a class Gauss schemes with staggered grids for HJ equation, based on Gauss schemes with staggered grids for conservation laws. The schemes are numerically tested on a variety of 1D and 2D problems; the solutions obtained in computation are satisfied.[KH3/4D]