On the stability of exponential fitting BDF algorithms

We present BDF type formulas capable of the exact integration (with only round-off errors) of differential equations whose solutions are linear combinations of an exponential with parameter λ and ordinary polynomials. For λ = 0 new formulas reduces to the classical BDF formulas. Plots of their 0-stability regions in terms of λ are provided. Plots of their regions absolute stability that include all the negative real axis are provided. Numerical examples shows the efficiency of the proposed codes, specially when we are integrating stiff oscillatory problems.