Research on actual or industrial applications of difference equations: a chimerical task?

• Published in: Journal of difference equations and applications Vol. 30; no. 10; pp. 1438 - 1492
• Main Author: Lozi, René
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.10.2024; Taylor & Francis Ltd
• Series: Special Issue dedicated to Saber Elaydi on the occasion of his 80th birthday
• Subjects: 39-02; actual applications; derivation method; Difference equations; Differential equations; discrete model; Dynamical Systems; geometric model; Industrial applications; Mathematics; Industrial applications; discrete dynamical systems; Difference equation; differential equations
• ISSN: 1023-6198; 1563-5120
• DOI: 10.1080/10236198.2023.2228926

Relationships between difference and differential equations are examined, to understand why the applications of the first to problems of real life, are not as well developed as the applications of the second. In this goal, a review of journals devoted to both types of equations is done, strengthened by the analysis of the MSC2020-Mathematics Subject Classification System. The screening of 296 Issues of the Journal of Difference Equations and Applications published since 1995 highlights that only a low ratio of the published papers are concerned with applications, even if this ratio is slightly increasing for 27 years. An analysis of first, what are possible relationships between actual problems and difference equations, and second, what could be an application of difference equations are discussed. Finally, some avenues of work to increase the number of applications are explored.