Numerical computation of the eigenvalues of a discontinuous Dirac system using the sinc method with error analysis

References

• S.M. Al-Harbi, On computing of eigenvalues of differential equations Q = λP with eigenparameter in boundary conditions, J. Math. Stat. 7 (2011), pp. 28–36..
   Google Scholar
• Annaby, M. H. , and Asharabi, R. M. , 2008. Approximating eigenvalues of discontinuous problems by sampling theorems , J. Numer. Math. 16 (2008), pp. 163–183.
   Web of Science ®Google Scholar
• Annaby, M. H. , and Asharabi, R. M. , 2008. On sinc-based method in computing eigenvalues of boundary-value problems , SIAM J. Numer. Anal. 46 (2008), pp. 671–690.
   Web of Science ®Google Scholar
• Annaby, M. H. , and Tharwat, M. M. , 2007. On computing eigenvalues of second-order linear pencils , IMA J. Numer. Anal. 27 (2007), pp. 366–380.
   Web of Science ®Google Scholar
• Annaby, M. H. , and Tharwat, M. M. , 2007. Sinc-based computations of eigenvalues of Dirac systems , BIT 47 (2007), pp. 699–713.
   Web of Science ®Google Scholar
• Annaby, M. H. , and Tharwat, M. M. , 2012. On the computation of the eigenvalues of Dirac systems , Calcolo 49 (2012), pp. 221–240.
   Web of Science ®Google Scholar
• Boumenir, A. , 2000. Higher approximation of eigenvalues by the sampling method , BIT 40 (2000), pp. 215–225.
   Web of Science ®Google Scholar
• Boumenir, A. , 2001. Sampling and eigenvalues of non-self-adjoint Sturm–Liouville problems , SIAM. J. Sci. Comput. 23 (2001), pp. 219–229.
   Web of Science ®Google Scholar
• Boumenir, A. , and Chanane, B. , 1996. Eigenvalues of S-L systems using sampling theory , Appl. Anal. 62 (1996), pp. 323–334.
   Google Scholar
• Butzer, P. L. , and Stens, R. L. , 1985. A modification of the Whittaker–Kotel'nikov–Shannon sampling series , Aequationes Math. 28 (1985), pp. 305–311.
   Google Scholar
• Butzer, P. L. , Schmeisser, G. , and Stens, R. L. , 2001. "An introduction to sampling analysis". In: Marvasti, F. , ed. Non Uniform Sampling: Theory and Practices . New York: Kluwer; 2001. pp. 17–121.
   Google Scholar
• Butzer, P. L. , Splettstösser, W. , and Stens, R. L. , 1988. The sampling theorem and linear prediction in signal analysis , Jahresber. Deutsch. Math.-Verein. 90 (1988), pp. 1–70.
   Google Scholar
• Chadan, K. , and Sabatier, P. C. , 1989. Inverse Problems in Quantum Scattering Theory . Berlin: Springer-Verlag; 1989.
   Google Scholar
• Chanane, B. , 2005. Computation of the eigenvalues of Sturm–Liouville problems with parameter dependent boundary conditions using the regularized sampling method , Math. Comput. 74 (252) (2005), pp. 1793–1801.
   Web of Science ®Google Scholar
• Chanane, B. , 2007. Computing the spectrum of non-self-adjoint Sturm–Liouville problems with parameter-dependent boundary conditions , J. Comput. Appl. Math. 206 (2007), pp. 229–237.
   Web of Science ®Google Scholar
• Chanane, B. , 2007. Computing the eigenvalues of singular Sturm–Liouville problems using the regularized sampling method , Appl. Math. Comput. 184 (2007), pp. 972–978.
   Web of Science ®Google Scholar
• Chanane, B. , 2007. Eigenvalues of Sturm–Liouville problems with discontinuity conditions inside a finite interval , Appl. Math. Comput. 188 (2007), pp. 1725–1732.
   Web of Science ®Google Scholar
• Chanane, B. , 2007. Sturm–Liouville problems with impulse effects , Appl. Math. Comput. 190 (2007), pp. 610–626.
   Web of Science ®Google Scholar
• Jagerman, D. , 1966. Bounds for truncation error of the sampling expansion , SIAM. J. Appl. Math. 14 (1966), pp. 714–723.
   Web of Science ®Google Scholar
• Kowalski, M. , Sikorski, K. , and Stenger, F. , 1995. Selected Topics in Approximation and Computation . New York: Oxford University Press; 1995.
   Google Scholar
• Levitan, B. M. , and Sargsjan, I. S. , 1975. Introduction to Spectral Theory: Self Adjoint Ordinary Differential Operators . Vol. 39. Providence, RI: American Mathematical Society; 1975, Translation of Mthematical Monographs.
   Google Scholar
• Levitan, B. M. , and Sargsjan, I. S. , 1991. Sturm–Liouville and Dirac Operators . Dordrecht: Kluwer Acadamic; 1991.
   Google Scholar
• Lund, J. , and Bowers, K. , 1992. Sinc Methods for Quadrature and Differential Equations . Philadelphia, PA: SIAM; 1992.
   Google Scholar
• Stenger, F. , 1981. Numerical methods based on Whittaker cardinal, or sinc functions , SIAM Rev. 23 (1981), pp. 156–224.
   Web of Science ®Google Scholar
• Stenger, F. , 1993. Numerical Methods Based on Sinc and Analytic Functions . New York: Springer-Verlag; 1993.
   Google Scholar
• Tharwat, M. M. , Yildirim, A. , and Bhrawy, A. H. , Sampling of discontinuous Dirac systems , Numer. Funct. Anal. Optim., accepted for publication, doi: 10.1007/s11075-012-9609-3..
   Web of Science ®Google Scholar