Functional Newton Solution of HJB in Continuous-Time Growth Models: Evidence from OECD Economies (2000–2025)

Abstract This paper develops a nonlinear continuous-time macroeconomic optimization framework based on functional Hamilton–Jacobi–Bellman dynamics with rigorous convergence properties. The study provides mathematical proof of quadratic convergence for a Newton-type functional solution method applied to equilibrium value function computation. The model integrates capital accumulation, consumption optimization, and welfare evaluation within a complex dynamic propagation structure. Empirical calibration is conducted using macroeconomic data from five advanced economies and a broader sample of Organisation for Economic Co operation and Development countries over the period 2000 to 2025. The framework jointly estimates structural parameters governing discounting behavior, risk sensitivity, depreciation dynamics, and capital production share. Simulation results demonstrate strong agreement between model predictions and observed macroeconomic indicators, with correlation coefficients exceeding 0.94 across major variables. Numerical experiments confirm that the proposed computational algorithm achieves rapid convergence, typically within a small number of iterations, while maintaining residual errors near machine precision. Phase diagram analysis and sensitivity tests show that the system operates within a globally stable nonlinear dynamic regime. Policy analysis indicates that productivity enhancement and uncertainty reduction generate the largest welfare improvements compared with structural preference adjustments. The continuous-time modelling approach provides a flexible tool for evaluating long run macroeconomic stabilization strategies. Overall, the study contributes to theoretical, computational, and empirical macroeconomic literature by establishing a robust complex dynamic equilibrium framework applicable to multi country economic analysis.