A Review of Differential Equations that is applicable to Differential Difference Equations

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Published: Sep 2, 2024
DOI: https://doi.org/10.29070/tx9tyb77
Keywords:
differential equations, differential difference equations, mathematical modeling, framework, dynamical systems, DDEs, systems with discrete time steps, delayed effects, ODEs, PDEs, ordinary differential equations, partial differential equations, analytical approaches, numerical strategies, continuous-time problems, physical systems, biological systems, engineering systems

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Authors

Naveen Kashyap

Ph.D. Scholar, ISBM University, Gariyaband, Chhattisgarh, India.

Abstract

Mathematical modeling relies heavily on differential equations because they offer a robustframework for studying and understanding dynamical systems. However, the study of differential differenceequations (DDEs) has evolved as a subfield within differential equations due to the increasing prevalence ofsystems with discrete time steps and delayed effects. The purpose of this work is to present a synopsisof research on differential equations that may be used in the analysis of differential difference equations.The review starts with a thorough introduction to ODEs and PDEs (ordinary and partial differentialequations). Fundamental ideas, analytical approaches, and numerical strategies for solving thesecontinuous-time problems are discussed. ODEs and PDEs are highlighted for their importance insimulating a wide range of physical, biological, and engineering systems.

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Issue

Vol. 20 No. 1 (2023): Journal of Advances in Science and Technology (JAST)

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