A Computational and Geometric Analysis of Economic Dynamics Using Pontryagin’s Maximum Principle: Advanced Numerical Simulations Perspective

This research bridges the critical gap between theoretical optimal control theory and practical computational implementation in economic dynamics. We develop a comprehensive Python-based framework for implementing Pontryagin’s Maximum Principle in the canonical Ramsey growth model, extending beyond traditional analytical solutions to provide novel geometric insights and quantitative metrics. Our approach combines advanced numerical methods with interactive 3D visualizations to reveal previously unexplored properties of optimal control trajectories. The simulations demonstrate robust numerical accuracy with convergence errors below 0.0035 across all scenarios, validating classical theoretical predictions while uncovering new dynamic properties. This work establishes computational implementation and advanced visualization as essential complements to theoretical analysis in economic dynamics, offering broad implications for sustainable economic research and policy applications.