Correction

This article refers to:

Numerical computation of the eigenvalues of a discontinuous Dirac system using the sinc method with error analysis

Article title: Numerical computation of the eigenvalues of a discontinuous Dirac system using the sinc method with error analysis

Authors: Tharwat, M. M., Bhrawy, A. H., & Yildirim, A.

Journal: International Journal of Computer Mathematics

Bibliometrics: Volume 89, Number 15, pages 2061-2080

DOI: https://doi.org/10.1080/00207160.2012.700112

Note that, two of the co-authors (Tharwat and Yildirim) are making this correction as the third co-author (A. H. Bhrawy) is deceased.

A reference to work by Al-Harbi (2011) and an updated version of the work by Annaby and Tharwat (2012) were inadvertently omitted from the original article. The following corrections have been made to the online version of the article.

The following text has been added after the first paragraph on p. 2062:

The problem (1)–(5) is well-defined and its solutions exist and are unique, see [25, pp. 328-329]. For functions $u(x),$which defined on [−1, 0) $\cup$ [ (0, 1] and has finite limit u(±0) := $\underset{x\to \pm 0}{lim}u(x)$ , are defined in [25, p. 327]. In this paper, we are interested in two types of generalizations of the problem in [5]. First, we wish to consider more general differential equations, for which $p_1(x)$ and $p_2(x)$ may have a discontinuity at one inner point of the considered interval. The second generalization that we discuss in this study concerns the point of discontinuity $x=0$, at which two supplementary transmission conditions are given. In addition, using computable error bounds, we obtain eigenvalue enclosures, which did not exist in [5], in a simple way, see Section 3 below.

The following text has been added to the last paragraph on p. 2062 in the original article:

In [26], the author computed approximately the eigenvalues of second order operator pencil using sinc method. The author here considers only truncation error, although amplitude error appears here too.

Reference [5] in the original article has been updated to:

[5] M.H. Annaby and M.M. Tharwat, On the computation of the eigenvalues of Dirac systems, Calcolo, 49 (2012), pp. 221-240.

The following reference has been added to the article:

[26] S.M. Al-Harbi, On computing of eigenvalues of differential equations Q = P with eigenparameter in boundary conditions, Journal of Mathematics and Statistics, 7 (2011), pp. 28-36.