Each Runge-Kutta-Fehlberg step requires the use of the following six values:
Then an approximation to the solution of the I.V.P. is made using a Runge-Kutta method of order 4:
And a better value for the solution is determined using a Runge-Kutta method of order 5:
The optimal step size sh can be determined by multiplying the scalar s times the current step size h. The scalar s is
where is the specified error control tolerance.