Concepts of Delay Differential Equations and Numerical Solution Methods
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This article provides a detailed introduction to the concepts of delay differential equations, including their definitions, characteristics, and classifications, while comprehensively explaining the principles and applications of numerical solution methods. We present specific computational examples and detailed implementation approaches in MATLAB to help beginners better understand and master relevant knowledge. The implementation includes code demonstrating Euler-type methods and Runge-Kutta adaptations for handling delayed terms, with special attention to interpolation techniques for non-grid delay values. Additionally, we provide complete source code for readers' reference and study. Furthermore, we introduce practical application scenarios of delay differential equations in fields like biological systems and control engineering, and explore their application prospects across different domains to help readers gain deeper insights into this field.
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