The most often used method of the Runge-Kutta family is the Fourth-Order one, which extends the idea of the mid-point method, by jumping 1/4th of the way first, then going half-way, a la the mid-point method, then going 3/4th of the way and finally juping all the way.

The formula for this method looks as follows:

k_{1} |
= | ||

k_{2} |
= | ||

k_{3} |
= | ||

k_{4} |
= | ||

x_{n+1} |
= |