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DOI:http://dx.doi.org/10.26855/jamc.2022.06.006

Accurate and Efficient Computations of the Gordeyev Integral

Date: June 1,2022 |Hits: 190 Download PDF How to cite this paper

 Mofreh R. Zaghloul

Department of Physics, College of Sciences, United Arab Emirates University, Al-Ain, 15551, UAE.

*Corresponding author:  Mofreh R. Zaghloul

Abstract

Investigation of the dispersion properties of plasma waves and associated phenomena is important in many fields of science. The dispersion relation of a magnetized hot Maxwellian plasma can be expressed in terms of the transcendental Gordeyev integral,  with R (ν)>0. In a general physical situation, the variables ν,ω and λ are complex. An accurate and efficient algorithm to calculate this transcendental integral is missing in the literature. In this paper, we present two accurate algorithms to calculate this important function: (a) a reference algorithm in which the Gordeyev integral is reformulated in terms of equivalent integrals of real functions where standard adaptive quadrature can be used to evaluate the integrals; and (b) an accurate and relatively efficient algorithm, in terms of an infinite series sum, employing recent developments in the calculation of the Faddeyeva or plasma dispersion function. The present algorithms can be implemented in any software package or any programming language. Validation and reliability of the present algorithms have been established through comparison between the two independent techniques in several computational platforms including modern Fortran, MapleTM 2015 and MatlabTM in addition to comparison with results of some practical physical problems existing in the literature.

References

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How to cite this paper

Accurate and Efficient Computations of the Gordeyev Integral

How to cite this paper:  Mofreh R. Zaghloul. (2022) Accurate and Efficient Computations of the Gordeyev Integral. Journal of Applied Mathematics and Computation6(2), 219-229.

DOI: http://dx.doi.org/10.26855/jamc.2022.06.006

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