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Numerical Algorithms for Computing Eigenvalues of Discontinuous Dirac System Using Sinc‐Gaussian Method

Author

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  • A. H. Bhrawy
  • M. M. Tharwat
  • A. Al-Fhaid

Abstract

The eigenvalues of a discontinuous regular Dirac systems with transmission conditions at the point of discontinuity are computed using the sinc‐Gaussian method. The error analysis of this method for solving discontinuous regular Dirac system is discussed. It shows that the error decays exponentially in terms of the number of involved samples. Therefore, the accuracy of the new method is higher than the classical sinc‐method. Numerical results indicating the high accuracy and effectiveness of these algorithms are presented. Comparisons with the classical sinc‐method are given.

Suggested Citation

  • A. H. Bhrawy & M. M. Tharwat & A. Al-Fhaid, 2012. "Numerical Algorithms for Computing Eigenvalues of Discontinuous Dirac System Using Sinc‐Gaussian Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:925134
    DOI: 10.1155/2012/925134
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    References listed on IDEAS

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    1. Ahmad Imani & Azim Aminataei & Ali Imani, 2011. "Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-11, May.
    2. A. H. Bhrawy & A. S. Alofi & S. I. El-Soubhy, 2011. "Spectral Shifted Jacobi Tau and Collocation Methods for Solving Fifth-Order Boundary Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-14, July.
    3. A. H. Bhrawy & A. S. Alofi & S. I. El-Soubhy, 2011. "Spectral Shifted Jacobi Tau and Collocation Methods for Solving Fifth‐Order Boundary Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
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    Cited by:

    1. M. M. Tharwat & A. H. Bhrawy & A. S. Alofi, 2013. "Computing Eigenvalues of Discontinuous Sturm‐Liouville Problems with Eigenparameter in All Boundary Conditions Using Hermite Approximation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Mohammed M. Tharwat & Mohammed A. Alghamdi, 2014. "Computation of Spectral Parameter of Discontinuous Dirac Systems with a Gaussian Multiplier," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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