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

Naveen Kashyap*, in Journal of Advances in Science and Technology | Science & Technology


Mathematical modeling relies heavily on differential equations because they offer a robust framework for studying and understanding dynamical systems. However, the study of differential difference equations (DDEs) has evolved as a subfield within differential equations due to the increasing prevalence of systems with discrete time steps and delayed effects. The purpose of this work is to present a synopsis of 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 differential equations). Fundamental ideas, analytical approaches, and numerical strategies for solving these continuous-time problems are discussed. ODEs and PDEs are highlighted for their importance in simulating a wide range of physical, biological, and engineering systems.