Skip to main content

Smooth and discrete systems—algebraic, analytic, and geometrical representations

Abstract

What is a differential equation? Certain objects may have different, sometimes equivalent representations. By using algebraic and geometrical methods as well as discrete relations, different representations of objects mainly given as analytic relations, differential equations can be considered. Some representations may be suitable when given data are not sufficiently smooth, or their derivatives are difficult to obtain in a sufficient accuracy; other ones might be better for expressing conditions on qualitative behaviour of their solution spaces. Here, an overview of old and recent results and mainly new approaches to problems concerning smooth and discrete representations based on analytic, algebraic, and geometrical tools is presented.

Author information

Affiliations

Authors

Corresponding author

Correspondence to František Neuman.

Rights and permissions

This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

About this article

Cite this article

Neuman, F. Smooth and discrete systems—algebraic, analytic, and geometrical representations. Adv Differ Equ 2004, 791318 (2004). https://doi.org/10.1155/S1687183904401034

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1155/S1687183904401034