Sinc-regularized techniques to compute eigenvalues of schrödinger operators on L2(I)⊕ℂ2

We introduced two different sinc-regularized techniques to compute eigenvalues of Schrödinger operators defined on the Hilbert space L 2 ( 0 , 1 ) ⊕ ℂ 2 because of the appearance of eigenvalue parameter in the boundary conditions. Both techniques improve significantly the error estimates resulting f...

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Bibliographic Details
Published in:Numerical algorithms 2019-03, Vol.80 (3), p.795-817
Main Authors: Annaby, M. H., Tharwat, M. M.
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Boundary conditions
Computer Science
Eigenvalues
Error analysis
Hilbert space
Mathematical functions
Mathematics
Numeric Computing
Numerical Analysis
Operators (mathematics)
Original Paper
Theory of Computation
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Summary:We introduced two different sinc-regularized techniques to compute eigenvalues of Schrödinger operators defined on the Hilbert space L 2 ( 0 , 1 ) ⊕ 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.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-018-0507-1