Gradients of local linear hulls in finite-difference operators for the Hamilton-Jacobi equations

Autor:	N.V. Mel'nikova, Alexander M. Tarasyev
Rok vydání:	1997
Předmět:	Operator (computer programming) Local linear Mechanics of Materials Applied Mathematics Mechanical Engineering Modeling and Simulation Scheme (mathematics) Hull Mathematical analysis Regular polygon Finite difference operator Hamilton–Jacobi equation Mathematics
Zdroj:	Journal of Applied Mathematics and Mechanics. 61:409-417
ISSN:	0021-8928
DOI:	10.1016/s0021-8928(97)00052-x
Popis:	A finite-difference operator (FDO) for the Hamilton-Jacobi equation is presented in which the non-existent solution gradients are replaced by the gradients of linear hulls. The approximation scheme (AS) corresponding to this FDO is proved to be minorized and majorized by ASs with FDOs based on the construction of sub-differentials and superdifferentials of local convex and concave hulls. This makes it possible to verify that the ASs converge to the linear constructions. Modifications of the FDO taking into account the configuration of local attainability domains are considered. The results of numerical experiments are presented.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::6adbda0c72e896fbfb327cc1345db5e6 https://doi.org/10.1016/s0021-8928(97)00052-x Zobrazit plný text záznamu Full Text from ScienceDirect