Regularized exponentially fitted methods for oscillatory problems

The aim of this work is to regularize the expression of the coefficients, expressed in term of trigonometrical or hyperbolic functions, arising from the exponential fitting procedure, by reformulating them in terms of the so-called ηm functions. These coefficients are functions of the variable ν = ωh where ω is the frequency and h is the step size. This reformulation eliminates the 0/0 indeterminate form of the coefficients when ν tends to 0. This procedure makes the methods more accurate. A numerical evidence is also given.