On the Leading Error Term of Exponentially Fitted Numerov Methods

Second-order boundary value problems are solved with exponentially-fitted Numerov methods. In order to attribute a value to the free parameter in such a method, we look at the leading term of the local truncation error. By solving the problem in two phases, a value for this parameter can be found such that the tuned method behaves like a sixth order method. Furthermore, guidelines to choose between multiple possible values for this parameter are given.