Runge-Kutta Method Algorithm

The Runge-Kutta methods are a family of techniques for numerically solving ordinary differential equations by estimating the solution's value at successive steps forward in time, using a weighted combination of several trial slope estimates computed within each step rather than a single slope estimate as in the simpler Euler method. The most commonly used member of the family, often called simply the Runge-Kutta method or RK4, evaluates four such slope estimates per step and achieves fourth-order accuracy. The methods are named for the German mathematicians Carl Runge and Wilhelm Kutta, who developed them around 1900.