(untitled) (INTERNATIONAL CONFERENCE ON ANALYSIS OF MATHEMATICS AND EXACT SCIENCES, 2025)
Inflation modeling is a critical area of research in economic analysis, enabling policymakers and analysts to predict and control inflationary trends effectively. This paper provides a comparative overview of advanced differential equation-based mathematical models used in inflation estimation, including the Poisson equation, the heat equation, Navier-Stokes equations, Hamilton-Jacobi-Bellman (HJB) equation, Kalman filtering, and stochastic differential equations (SDEs). The paper also introduces numerical methods, such as finite difference and iterative algorithms, for solving these models. A concrete example problem related to regional inflation variations is explored, showcasing numerical solutions for better understanding and implementation.