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A sinc-Gaussian solver for general second order discontinuous problems

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Abstract

The sinc-Gaussian sampling operator has become an efficient tool in interpolating entire and analytic functions with appropriate growth properties. It accelerates the rate of convergence and remarkably enhance the slow rate of convergence of the classical sinc method. In this paper we compute the eigenvalues of discontinuous second order boundary-value problems using the sinc-Gaussian sampling technique. The problem is defined in two ways throughout \([-1,1]\) and is not in general self adjoint. The boundary and compatibility conditions are assumed to be regular in the sense of Birkhoff to guarantee the existence and discreteness of the eigenvalues, which are in general complex numbers and are not necessarily simple. Numerical examples are worked out with graphical illustrations and comparisons with the classical sinc-technique.

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Acknowledgements

This research is partially supported by Alexander von Humboldt foundation under the Grants 3.4-EGY/1039259 and 3.4-JEM/1142916.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, 12613, Giza, Egypt

    M. H. Annaby

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

    R. M. Asharabi

Authors
  1. M. H. Annaby
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  2. R. M. Asharabi
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Correspondence to M. H. Annaby.

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Annaby, M.H., Asharabi, R.M. A sinc-Gaussian solver for general second order discontinuous problems. Japan J. Indust. Appl. Math. 35, 653–668 (2018). https://doi.org/10.1007/s13160-018-0305-0

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  • DOI: https://doi.org/10.1007/s13160-018-0305-0

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