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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Structured Shamanskii methods for Chandrasekhar equation arising from radiation; pp. 97–108

(Full article in PDF format) https://doi.org/10.3176/proc.2020.2.01


Authors

Ning Dong, Bo Yu, Zhaoyun Meng

Abstract

The Chandrasekhar equation describes the particles emerging from the atmospheric radiation and its solution of physical significance is the minimal positive solution. This paper analyses the efficiency index of Newton’s iteration in detail, which then helps to design a structured Shamanskii method for calculating the minimal positive solution. The monotone convergence of the presented algorithm is subsequently established as well as the elementary monotonicity of the solution. Preliminary numerical experiments are listed to indicate that the newly developed two-step structured Shamanskii method outperforms the Newton’s method in terms of CPU time and iterative number with almost no loss in accuracy.

Keywords

Chandrasekhar equation, Newton’s method, structured Shamanskii method, factor-alternating direction implicit iteration.

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Current Issue: Vol. 69, Issue 2, 2020




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December