Im trying to understand the linked paper (cf paper), please correct me if my understanding is wrong !
Im looking to get an interpolation function from the result of a Dormand Prince (RK45) integration step, first introduced in the paper. In order to get the polynomial coefficients, it is said that only 3 equations need to be solved in order to get the interpolant's coefficients.
If the step was from $t_n$ to $t_{n+1}$, then the interpolant would be written as
$y(t_n + \sigma h) = y_n + (\sigma h) \sum_0^7 \alpha_j k_j \quad \sigma \in [0,1]$
where $k_j$ are Dopri's RK coefficients, $h$ the stepsize and the $\alpha_j$s are what we need to compute to get the interpolant.
Now this is where I'm lost, how do you compute the $\alpha_j$ ?
Thanks