The term "differential equations" refers to mathematical equations involving derivatives of one or more unknown functions. They describe dynamic processes and changes over time or in relation to other variables. Differential equations are widely used in engineering, science, and economics—for example, to model growth, physical systems, control loops, or financial developments.
Solving initial and boundary value problems: Numerical or symbolic methods for computing solutions based on defined initial or boundary conditions.
Symbolic solution of differential equations: Calculation of exact analytical solutions when possible.
Numerical integration: Use of methods such as Runge-Kutta or Euler for approximate solutions of equation systems.
Modeling dynamic systems: Representation of physical, biological, or technical processes using systems of differential equations.
Visualization of solutions: Graphical display of function curves, phase portraits, or trajectories to illustrate results.
Stability analysis: Examination of the long-term behavior of solutions, e.g., near equilibrium states.
System simulation: Simulation of complex systems (e.g., electrical circuits, mechanical structures) based on differential equations.
Model export: Capability to export developed equation systems into programming languages or simulation environments.
An engineering firm calculates the vibration of a spring-mass system using a second-order linear differential equation.
A pharmaceutical company simulates drug concentration in the bloodstream over time using a system of coupled differential equations.
A financial services provider models interest rate developments over time using stochastic differential equations.
A mechanical engineering company analyzes machine temperature behavior by solving the heat conduction equation.
A software developer visualizes the trajectory of the Lotka-Volterra model (predator-prey dynamics) to analyze biological interactions.
