Such models, represented by ordinary differential equations (ODEs), underpin numerous scientific and engineering disciplines by describing the evolution of physical, chemical or biological processes.

Model natural and engineered hydraulic and hydrologic systems. Manage large datasets and develop models for hydrodynamics. Gain in-depth modeling experience using real-world case studies in a ...

APPM 5460 Methods in Applied Mathematics: Dynamical Systems and Differential Equations Introduces the theory and applications of dynamical systems through solutions to differential equations.Covers ...

Real impact for quality of life Heitzinger’s research project, “Partial-Differential-Equations Models for Nanotechnology,” aims to develop mathematical models and simulation tools for new applications ...

The connection structure of the discrete system tends to be richer than that of the integro-differential equation model; however, the continuum problem can be studied analytically using traveling wave ...

Even if the differential equations that govern these systems can be solved — and they often can't — it usually is impossible to use the results to predict the behavior of the system, Platzer said.

For the description of complex dynamical systems, data-driven modeling and AI are gaining increasing importance. In this context, large data sets from experiments and computer simulations are ...

Technical Terms Differential Equation Models: Mathematical formulations that describe the rate of change of a system’s state variables through equations involving derivatives.

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by ...