Runge-Kutta is a set of numerical methods for approximating the solutions of differential equations. A differential equation is an equation that consists of the derivative of a variable (think the rate of change) defined in terms of another, independent variable (think physical property). For example, consider a virus. As a virus spreads, its rate of infection becomes faster and faster. The same is true for population growth in most species. Most often used in such fields as biology, engineering, physics, and economics, differential equations are extremely handy for expressing complex systems. Unfortunately, only the most trivial of differential equations can be explicitly solved. For the rest, we use numerical methods such as Runge-Kutta, which was developed by mathematicians Carl Runge and Wilhelm Kutta.
While Runge-Kutta is technically a set of numerical methods...
