Advances in Difference Equations
Volume 2006 (2006), Article ID 43092, 19 pages
doi:10.1155/ADE/2006/43092

On discrete analogues of nonlinear implicit differential equations

Abstract

This paper deals with some classes of nonlinear implicit difference equations obtained via discretization of nonlinear differential-algebraic or partial differential-algebraic equations. The unique solvability of discretized problems is proved and the compatibility between index notions for nonlinear differential-algebraic equations and nonlinear implicit difference equations is studied.