Many branches of Physics and Engineering use perturbed linear ODELs. One method of resolution is based on the use of Scheifele functions for systems. This paper systematically expands three applications of the Scheifele method adapted to stiff problems. For this purpose, a family of matrices, Г-functions and the numerical method are presented for the integration of perturbed linear systems with constant coefficients, which enables the solution to be expressed as a series of Г-functions. The series coefficients are obtained through recurrence relations involving the perturbation function. One of the main difficulties in terms of implementing the method is the need to determine these relations for each case.
Furthermore, in this paper, the necessary adaptations are made in order to facilitate the calculation of the recurrence relations required for system integration. In each problem, the numerical algorithm is designed with a view to enabling computational implementation. This algorithm presents the same good properties as the integration method for harmonic oscillators, in other words it can accurately integrate the non-perturbed problem using just the first term in the series.
The results show increased accuracy in the application of the model when compared to other known methods implemented in Maple V.