GRADIENTS OF LOCAL LINEAR HULLS IN FINITE-DIFFERENCE OPERATORS FOR THE HAMILTON-JACOBI EQUATIONS

A finite-difference operator (FDO) for the Hamilton-Jacobi equation is presented in which the non-existent solution gradients are replaced b y the gradients of linear hulls. The approximation scheme (AS) corresp onding to this FDO is proved to be minorized and majorized by ASs with FDOs based on the construction of sub-differentials and superdifferen tials of local convex and concave hulls. This makes it possible to ver ify that the ASs converge to the linear constructions. Modifications o f the FDO taking into account the configuration of local attainability domains are considered. The results of numerical experiments are pres ented. (C) 1997 Elsevier Science Ltd. All rights reserved.