International Journal of Scientific Research and Engineering Development

Mathematical modelling using differential equations plays a vital role in understanding and analysing dynamic real-world phenomena across disciplines such as engineering, biology, environmental science, and economics. The present study focuses on the formulation, analysis, and application of differential equation–based models to represent complex systems characterized by continuous change over time and space. Both ordinary and partial differential equations are employed to capture nonlinear interactions, diffusion processes, stability behavior, and sensitivity to parameter variations. The research integrates analytical techniques with numerical simulation methods to obtain meaningful solutions for models that are otherwise difficult to solve in closed form. Stability analysis, bifurcation behavior, and qualitative dynamics are examined to understand equilibrium conditions and long-term system evolution. The results demonstrate that differential equation modelling provides reliable insights into system performance, enabling prediction, optimization, and control of real-life processes such as population growth, heat transfer, and ecological interactions. Furthermore, the study highlights the importance of parameter estimation, computational efficiency, and validation using empirical data to enhance model accuracy. The findings emphasize the interdisciplinary relevance of mathematical modelling and suggest future directions involving hybrid computational approaches and multiscale frameworks for improved real-world applicability.

Dr.Sarita,"Mathematical Modelling of Real-World Problems Using Differential Equations" International Journal of Scientific Research and Engineering Development, V9(3): Page(976-990) May-June 2026. ISSN: 2581-7175. www.ijsred.com. Published by Scientific and Academic Research Publishing.