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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.

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Correspondence to Pham Ky Anh.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Anh, P.K., Loi, L.C. On discrete analogues of nonlinear implicit differential equations. Adv Differ Equ 2006, 043092 (2006). https://doi.org/10.1155/ADE/2006/43092

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation