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.
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