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Numerical Algorithms

, Volume 80, Issue 3, pp 795–817 | Cite as

Sinc-regularized techniques to compute eigenvalues of schrödinger operators on \(L^{2}(I)\oplus \mathbb {C}^{2}\)

  • M. H. AnnabyEmail author
  • M. M. Tharwat
Original Paper
  • 27 Downloads

Abstract

We introduced two different sinc-regularized techniques to compute eigenvalues of Schrödinger operators defined on the Hilbert space \(L^{2}(0,1)\oplus \mathbb {C}^{2}\) because of the appearance of eigenvalue parameter in the boundary conditions. Both techniques improve significantly the error estimates resulting from using the classical sampling method. Furthermore, it treats completely the obstacle that, for some potentials, integrals resulting from applying the sinc method cannot be explicitly computed. We derive a rigorous error analysis that takes into account both truncation and perturbation errors. Results are exhibited numerically and graphically with comparisons.

Keywords

Sinc-Gaussian method Sinc method Eigenvalue problem with eigenparameter in the boundary conditions Truncation and amplitude errors 

Mathematics Subject Classification (2010)

34L16 94A20 65L15 

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Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceCairo UniversityGizaEgypt
  2. 2.Department of Mathematics, Faculty of ScienceBeni-Suef UniversityBeni-SuefEgypt

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