Can you clarify what you mean by "Store the values of ε"? Do you want us to save a copy of every ε(x_i) for all 0 < i < N - 1?
That is, should we store out output as a 2x(N-1) matrix with one row for the ε values and the other for V values?
Yes, you should store all epsilon(x_i). You shouldn't as a 2x(N-1) matrix thought, rather, you should store two arrays separately in the same netcdf file.