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 (derivative)
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 (derivative_a, derivative_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.