Numerical computation of the coefficients in exponential fitting

We show that a direct numerical computation of the coefficients of any method based on the exponential fitting is possible. This makes unnecessary the knowledge of long sets of analytical expressions for the coefficients, as usually presented in the literature. Consequently, the task of any potential user for writing his/her own code becomes much simpler. The approach is illustrated on the case of the Numerov method for the Schrödinger equation, on a version for which the analytic expressions of coefficients are not known.