Runge-Kutta methods

Runge-Kutta methods are numerical techniques used to solve ordinary differential equations, which describe how a variable changes over time. Instead of finding exact solutions, these methods approximate the solution step-by-step. The most common version, the fourth-order Runge-Kutta method, calculates an average of several slopes at different points within each time step to improve accuracy. This allows us to track the behavior of systems in fields like physics, engineering, and finance, where precise predictions of change are essential. These methods are widely used due to their balance between simplicity and accuracy.