## The use of the generalized sinc-Gaussian sampling for numerically computing eigenvalues of periodic Dirac system

Rashad M. Asharabi and Mohammed M. Tharwat

### Abstract

The generalized sinc-Gaussian sampling operator is established by Asharabi (2016) to approximate two classes of analytic functions. In this paper, we use this operator to construct a new sampling method to approximate the eigenvalues of the periodic (semi-periodic) Dirac system of differential equations problem. The convergence rate of this method is of exponential type, i.e., $\mathrm{e}^{-\alpha_{r} N}/\sqrt{N}$, $\alpha_{r}=\left((r+1)\pi-\sigma h\right)/2$. The sinc-Gaussian and Hermite-Gauss methods are special cases of this method. We estimate the amplitude error associated to this operator, which gives us the possibility to establish the error analysis of this method. Various illustrative examples are presented and they show a good agreement with our theoretical analysis.

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### Key words

Generalized sinc-Gaussian, eigenvalues, periodic Dirac system, convergence rate.

### AMS subject classifications

30E10, 34L15, 47E05, 41A25, 94A20, 41A80.

### Links to the cited ETNA articles

 [5] Vol. 46 (2017), pp. 359-374 Rashad M. Asharabi: Approximating eigenvalues of boundary value problems by using the Hermite-Gauss sampling method

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