The use of the generalized sinc-Gaussian sampling for numerically computing eigenvalues of periodic Dirac system. ETNA - Electronic Transactions on Numerical Analysis
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13 novembre 2018
- handle: 10670/1.8qk9y1
- issn: 1068-9613
- doi: 10.1553/etna_vol48s373
info:eu-repo/semantics/openAccess
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Mohammed M. Tharwat et al., « The use of the generalized sinc-Gaussian sampling for numerically computing eigenvalues of periodic Dirac system. ETNA - Electronic Transactions on Numerical Analysis », Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschafte, ID : 10.1553/etna_vol48s373
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The generalized sinc-Gaussian sampling operator is established by Asharabi(2016) to approximate two classes of analytic functions. In this paper, weuse this operator to construct a new sampling method to approximate theeigenvalues of the periodic (semi-periodic) Dirac system of differentialequations problem. The convergence rate of this method is of exponentialtype, i.e., $\\mathrm{e}^{-\\alpha_{r} N}/\\sqrt{N}$,$\\alpha_{r}=\\left((r+1)\\pi-\\sigma h\\right)/2$. The sinc-Gaussian andHermite-Gauss methods are special cases of this method.We estimate the amplitude error associated to this operator, which gives us the possibility to establish the error analysis of this method.Various illustrative examples are presented and they show a good agreement with our theoretical analysis.