Mathematical Models and Simulations, 2nd Edition

This Reprint continues the work initiated in our previous edition, Mathematical Models and Simulations, emphasizing the central role of mathematical modeling in understanding complex systems across physics, biology, finance, and engineering. Mathematical models provide the structural framework through which the behavior of physical and abstract phenomena can be interpreted, predicted, and optimized. Alongside these theoretical foundations, numerical simulations serve as a crucial complement, enabling researchers to explore system dynamics, test hypotheses, and forecast quantities of interest with high fidelity.The Reprint brings together contributions spanning a broad spectrum of mathematical physics, highlighting both deterministic and stochastic modeling approaches. Deterministic models typically rely on ordinary or partial differential equations to describe well-defined system evolutions, while stochastic models account for randomness through stochastic processes or stochastic differential equations. Emphasis is placed on rigorous mathematical analyses of these models to ensure clarity, reliability, and applicability.