The study of nonlinear differential equations is crucial for understanding and predicting behaviors in multiscale complex systems, which are prevalent in fields such as physics, biology, and engineering. This research aims to develop advanced mathematical techniques to effectively model and analyze these systems. By integrating methods from functional analysis and computational mathematics, we designed a series of algorithms capable of addressing the intrinsic complexities and non-linearities present in such equations. Our findings demonstrate that these algorithms significantly improve the accuracy and efficiency of solving high-dimensional problems, providing deeper insights into the system dynamics. We also explored the application of these techniques in modeling ecological systems, where multiple interacting species often lead to unpredictable outcomes. The results showcase the potential of our approach in offering precise simulations of real-world phenomena, thus contributing to better decision-making processes in science and engineering. In conclusion, this work not only advances the theoretical framework of applied mathematics but also presents practical tools for tackling complex, nonlinear problems across various domains.