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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