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An Overview of the Computation of the Eigenvalues Using Sinc-Methods

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New Sinc Methods of Numerical Analysis

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Abstract

In this chapter we give a survey for the use of sinc methods in computing eigenvalues of various types of boundary value problems. The techniques cover the classical sinc-method, regularized sinc-method, Hermite interpolations and the associated regularized technique, sinc-Gaussian, Hermite-Gauss and generalized sinc-Gaussian methods. The application of these methods covers a very wide class of problems, involving, but not limited to, second order differential operators, λ-type problems in \(L^{2}(a,b)\oplus \mathbb {C}^{r}\) spaces, discontinuous problems, multiparameter problems, in self-adjoint and non self-adjoint settings, regular and singular problems. Both horizontal and vertical extensions of the application of the technique are still open and under consideration.

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Authors and Affiliations

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

    M. H. Annaby

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

    R. M. Asharabi

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

    M. M. Tharwat

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  1. M. H. Annaby
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  2. R. M. Asharabi
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  3. M. M. Tharwat
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Correspondence to M. H. Annaby .

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  1. Mathematics Department, German University in Cairo, New Cairo City, Egypt

    Gerd Baumann

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Annaby, M.H., Asharabi, R.M., Tharwat, M.M. (2021). An Overview of the Computation of the Eigenvalues Using Sinc-Methods. In: Baumann, G. (eds) New Sinc Methods of Numerical Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-49716-3_10

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