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Numerical algorithms for computing eigenvalues of discontinuous Dirac system using sinc-Gaussian method. (English) Zbl 1250.65135
Summary: The eigenvalues of a discontinuous regular Dirac systems with transmission conditions at the point of discontinuity are computed using the sinc-Gaussian method. The error analysis of this method for solving discontinuous regular Dirac system is discussed. It shows that the error decays exponentially in terms of the number of involved samples. Therefore, the accuracy of the new method is higher than the classical sinc-method. Numerical results indicating the high accuracy and effectiveness of these algorithms are presented. Comparisons with the classical sinc-method are given.
MSC:
65N25Numerical methods for eigenvalue problems (BVP of PDE)
65N15Error bounds (BVP of PDE)
35Q40PDEs in connection with quantum mechanics
81Q05Closed and approximate solutions to quantum-mechanical equations
35P15Estimation of eigenvalues and upper and lower bounds for PD operators