Just a few lines of code are sufficient for the numeric algorithms. They are applied in a loop as often as there are intervals. The end value of one loop is the initial value for the next one.

Parameters that are constant for all methods: 

Initial value (for x = 0)

Range of Variables

Number of intervals n

Width of intervals delta = Range/(n-1)

Variables x , y, first derivative (Ableitung)

specified for the methods by subscript, as xE, xH, xRK

Runge−Kutta uses intermediate values of the first derivative, which are specified by subscripts a und b (Ableitung_a, Ableitung_b)

Loops have an index i that runs from 0 to n, as xE[i]

F[i] are deviations of the numerical results from the analytic ones.