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Numerical computation of the eigenvalues of a discontinuous Dirac system using the sinc method with error analysis. (English) Zbl 1255.65144

Int. J. Comput. Math. 89, No. 15, 2061-2080 (2012); correction ibid. 98, No. 6, 1292 (2021).
Summary: We apply a regularized sinc method to compute the eigenvalues of a discontinuous regular Dirac system with transmission conditions at the point of discontinuity. The regularized technique allows us to insert some parameters to the well-known sinc method, strengthening the existing technique, and to avoid the aliasing error. The error analysis is established considering both the truncation and amplitude errors associated with the sampling theorem. Numerical examples together with tables and illustrative figures are given.

MSC:

65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
34L16 Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators
94A20 Sampling theory in information and communication theory
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References:

[1] DOI: 10.1515/JNUM.2008.008 · Zbl 1160.65039 · doi:10.1515/JNUM.2008.008
[2] DOI: 10.1137/060664653 · Zbl 1171.34059 · doi:10.1137/060664653
[3] DOI: 10.1093/imanum/drl026 · Zbl 1119.65076 · doi:10.1093/imanum/drl026
[4] DOI: 10.1007/s10543-007-0154-8 · Zbl 1131.65066 · doi:10.1007/s10543-007-0154-8
[5] Annaby M. H., Calcolo (2011)
[6] DOI: 10.1023/A:1022334806027 · Zbl 0957.65077 · doi:10.1023/A:1022334806027
[7] DOI: 10.1137/S1064827500374078 · Zbl 1006.34079 · doi:10.1137/S1064827500374078
[8] DOI: 10.1080/00036819608840486 · Zbl 0864.34073 · doi:10.1080/00036819608840486
[9] DOI: 10.1007/BF02189424 · Zbl 0582.41004 · doi:10.1007/BF02189424
[10] Butzer P. L., Non Uniform Sampling: Theory and Practices pp 17– (2001)
[11] Butzer P. L., Jahresber. Deutsch. Math.-Verein. 90 pp 1– (1988)
[12] DOI: 10.1007/978-3-642-83317-5 · doi:10.1007/978-3-642-83317-5
[13] DOI: 10.1090/S0025-5718-05-01717-5 · Zbl 1080.34010 · doi:10.1090/S0025-5718-05-01717-5
[14] DOI: 10.1016/j.cam.2006.06.014 · Zbl 1117.65117 · doi:10.1016/j.cam.2006.06.014
[15] DOI: 10.1016/j.amc.2006.05.187 · Zbl 1114.65095 · doi:10.1016/j.amc.2006.05.187
[16] DOI: 10.1016/j.amc.2006.11.082 · Zbl 1124.65066 · doi:10.1016/j.amc.2006.11.082
[17] DOI: 10.1016/j.amc.2007.01.092 · Zbl 1122.65378 · doi:10.1016/j.amc.2007.01.092
[18] DOI: 10.1137/0114060 · Zbl 0221.65200 · doi:10.1137/0114060
[19] Kowalski M., Selected Topics in Approximation and Computation (1995) · Zbl 0839.41001
[20] Levitan B. M., Introduction to Spectral Theory: Self Adjoint Ordinary Differential Operators 39 (1975)
[21] DOI: 10.1007/978-94-011-3748-5 · doi:10.1007/978-94-011-3748-5
[22] DOI: 10.1137/1.9781611971637 · doi:10.1137/1.9781611971637
[23] Stenger F., SIAM Rev. 23 pp 156– (1981)
[24] DOI: 10.1007/978-1-4612-2706-9 · doi:10.1007/978-1-4612-2706-9
[25] Tharwat M. M., Numer. Funct. Anal. Optim.
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