eprintid: 4682 rev_number: 5 eprint_status: archive userid: 351 dir: disk0/00/00/46/82 datestamp: 2016-01-15 02:06:51 lastmod: 2021-08-27 17:36:14 status_changed: 2016-01-15 02:06:51 type: article metadata_visibility: show item_issues_count: 1 creators_name: Papakov, G.V. creators_name: Tarasyev, A.M. creators_name: Uspenskii, A.A. creators_id: 7340 title: Numerical approximations for generalized solutions of Hamilton-Jacobi equations ispublished: pub internal_subjects: iis_met internal_subjects: iis_mod divisions: prog_dyn abstract: The Cauchy problem for a first-order partial differential equation whose left-hand side is a homogeneous function of the vector of derivatives, with the time derivative occurring additively, is considered. The boundary conditions are specified at the right end of the time interval. The solution of a differential game over a fixed time interval with a terminal functional is reducible to a problem of this type. The traditional difference method for constructing the solution of a boundary-value problem is not applicable, because the generalized solution need not be smooth. A mathematical technique, based on methods of solving game problems, is proposed. The resultant computational scheme, whose validity is established in three theorems, is based on a rectangular space mesh and a subdivision of the time interval. Unlike the classical approach, the scheme uses not finite differences but subdifferentials of the convex hulls of functions approximating the value function. date: 1996 date_type: published publisher: Elsevier id_number: 10.1016/S0021-8928(96)00072-X iiasapubid: XJ-96-019 iiasa_bibnotes: [in Russian] creators_browse_id: 1610 full_text_status: none publication: Applied Mathematics and Mechanics volume: 60 number: 4 pagerange: 570-581 refereed: TRUE issn: 0021-8928 coversheets_dirty: FALSE fp7_type: info:eu-repo/semantics/article citation: Papakov, G.V., Tarasyev, A.M. , & Uspenskii, A.A. (1996). Numerical approximations for generalized solutions of Hamilton-Jacobi equations. Applied Mathematics and Mechanics 60 (4) 570-581. 10.1016/S0021-8928(96)00072-X .