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Approximating eigenvalues of Dirac system with discontinuities at several points using Hermite-Gauss method

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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.

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Authors and Affiliations

  1. Department of Mathematics, College of Arts and Sciences, Najran University, Najran, Saudi Arabia

    Rashad M. Asharabi

  2. Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia

    Mohammed M. Tharwat

  3. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

    Mohammed M. Tharwat

Authors
  1. Rashad M. Asharabi
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  2. Mohammed M. Tharwat
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Correspondence to Rashad M. Asharabi.

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Asharabi, R.M., Tharwat, M.M. Approximating eigenvalues of Dirac system with discontinuities at several points using Hermite-Gauss method. Numer Algor 76, 655–673 (2017). https://doi.org/10.1007/s11075-017-0275-3

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  • DOI: https://doi.org/10.1007/s11075-017-0275-3

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