JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE) ›› 2018, Vol. 48 ›› Issue (1): 71-77.doi: 10.6040/j.issn.1672-3961.0.2017.085

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Numerical calculation method and distribution law of zero points of the compound Bessel function

JI Anzhao, WANG Yufeng*, LIU Xuefen   

  1. College of Energy Engineering, Longdong University, Qingyang 745000, Gansu, China
  • Received:2017-03-10 Online:2018-02-20 Published:2017-03-10

Abstract: In order to solve the problem of computing the zeros of compound Bessel functions, a modified optimization algorithm of the particle swarm and the quantum-behaved particle swarm were proposed. Most of the zero points of the compound Bessel function could be calculated by modified algorithm in the finite interval. In order to improve the searching ability of the zero points, the quantum-behaved particle swarm optimization algorithm with crossover operator was modified by using cross operator operation in combination with the characteristics of the two former algorithms. All the zero points of the compound Bessel function in the finite interval were found with the modified version of algorithm. The modified version of algorithm was faster with convergence rate and higher with zero points calculation accuracy. The calculation results showed that, except for the former three zero points, the following zero points showed linear relationship with their sequence on double logarithmic coordinate axis under the same parameters of the compound Bessel function. The straight-line fitting of the zero points and their sequence from different parameters was calculated. The results showed that the correlation coefficient was 99.99% and the relative error of zero point fitting was less than 0.5%, which could full fit the requirement of engineering calculation.

Key words: compound Bessel function, multimodal function, crossover operator, quantum particle swarm, finite reservoirs

CLC Number: 

  • TE32
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