scholarly journals Computation of Spectral Parameter of Discontinuous Dirac Systems with a Gaussian Multiplier

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Mohammed M. Tharwat ◽  
Mohammed A. Alghamdi
Keyword(s):  
Boundary Conditions ◽  
Spectral Parameter ◽  
Worked Examples ◽  
New Technique ◽  
Dirac System ◽  
Sinc Method ◽  
Dirac Systems

We aim in this paper to apply a sinc-Gaussian technique to compute the eigenvalues of a Dirac system which has a discontinuity at one point and contains a spectral parameter in all boundary conditions. We establish the needed properties of eigenvalues of our problem. The error of this method decays exponentially in terms of the number of involved samples. Therefore the accuracy of the new technique is higher than the classical sinc-method. Numerical worked examples with tables and illustrative figures are given at the end of the paper.

scholarly journals Numerical Algorithms for Computing Eigenvalues of Discontinuous Dirac System Using Sinc-Gaussian Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. H. Bhrawy ◽  
M. M. Tharwat ◽  
A. Al-Fhaid
Keyword(s):  
Error Analysis ◽  
Numerical Algorithms ◽  
High Accuracy ◽  
Transmission Conditions ◽  
Numerical Results ◽  
New Method ◽  
Dirac System ◽  
Sinc Method ◽  
Dirac Systems ◽  
Gaussian Method

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.

scholarly journals On the fractional Dirac systems with non-singular operators

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 2159-2168
Author(s):  
Ahu Ercan
Keyword(s):  
Laplace Transforms ◽  
Dirac System ◽  
Singular Operators ◽  
Dirac Systems

In this manuscript, we consider the fractional Dirac system with exponential and Mittag-Leffler kernels in Riemann-Liouville and Caputo sense. We obtain the representations of the solutions for Dirac systems by means of Laplace transforms.

The Parseval Equality and Expansion Formula for Singular Hahn-Dirac System

2020 ◽  
pp. 209-235
Author(s):  
Bilender P. Allahverdiev ◽  
Hüseyin Tuna
Keyword(s):  
Spectral Function ◽  
Spectral Parameter ◽  
Continuous Functions ◽  
Dirac System ◽  
Parseval Equality ◽  
Expansion Formula

This work studies the singular Hahn-Dirac system given by Here 𝜇 is a complex spectral parameter, p(.) and r(.) are real-valued continuous functions at 𝜔0, defined on [𝜔0,∞) and q∈(0,1), , 𝜔>0, x∈[𝜔0,∞). The existence of a spectral function for this system is proved. Further, a Parseval equality and an expansion formula in eigenfunctions are proved in terms of the spectral function.

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