A 2-D DIFFUSION-BASED POPULATION GROWTH MODEL USING CUBIC SPLINE NUMERICAL APPROXIMATION

Abstract

 This study presents a 2D diffusion model for population growth using a heat equation like partial differential equation. Population density changes over space and time are solved numerically with an explicit cubic spline interpolation scheme, giving smoother spatial estimates and better stability than basic finite differences. The model is validated with Surat city data using the 2001 census as the initial condition and comparing predictions to 2011 figures. Evaluation with RMSE and MAPE shows reasonable agreement and the framework can be extended to include spatially varying growth, migration and reaction diffusion effects.