Classical Runge-Kutta Method

The derivation of fourth order Runge-kutta methods involve tedious calculations. It transpires that with R=4, the fourth order and no higher can be obtained. The well-known fourth order classical Runge–Kutta method is given by

(3.30)

Remark: We have seen that there exists an R-stage method of order R and none of order greater than R for . We have the following result that relates the no. of stages in the Runge-Kutta process with the order of the method: