A numerically stable version of the P_N method for solving the one-speed problem of neutron transport in the exterior of a sphere is developed. A transformation is used to obtain a plane-geometry-like neutron transport equation, where the angular derivative part of the streaming term in spherical geometry is considered as a source. In this way, conventional P_N solutions developed for plane geometry can be used to solve the problem and avoid having to deal with ill-conditioned solutions expressed in terms of the modified spherical Bessel functions of the third kind.

中文翻译：

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关于球面几何中的P _N方法：球体外部的稳定解

开发了用于解决球体外部中子传输的单速问题的P _N方法的数值稳定形式。使用变换获得类似于平面几何的中子输运方程，其中将球形几何中的流项的角导数部分视为源。以这种方式，常规的P _Ñ为平面几何开发的解决方案可用于解决这个问题，并避免不必处理中的第三种改性球形贝塞尔函数来表示病态的解决方案。