Abstract
The Hermite-Gauss sampling method is established to approximate the eigenvalues of the continuous Sturm-Liouville problems in 2016. In the present paper, we apply this method to approximate the eigenvalues of the Dirac system with transmission conditions at several points of discontinuity. This method gives us a higher accuracy results in comparison with the results of other sampling methods (classical sinc, regularized sinc, Hermite, sinc-Gaussian). The error of this method decays exponentially in terms of number of involved samples. Illustrative examples have been discussed to show the effectiveness of the presented method. We compare our results with the results of sinc-Gaussian sampling method which was the best sampling method before the presented method.