Mathematical simulation is a computational method that uses formal mathematical models—such as systems of differential equations, stochastic processes, or optimization formulations—to numerically approximate the behavior of complex systems under specified conditions. It enables investigation of system dynamics, sensitivity to parameters, and emergent properties when analytical solutions are infeasible or intractable. Typical workflows include model specification, parameterization, numerical integration or iteration, and validation against empirical data. Mathematical simulations are central in fields such as physics, engineering, systems biology, and economics, supporting hypothesis testing, scenario analysis, and predictive inference while explicitly encoding assumptions about structure, interactions, and boundary conditions.
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