The radiative–conductive transfer equation in the $$S_N$$ approximation for spherical geometry is solved using a modified decomposition method. The focus of this work is to show how to distribute the source terms in the recursive equation system in order to guarantee arithmetic stability and thus numerical convergence of the obtained solution, guided by a condition number criterion. Some examples are compared with results from literature and parameter combinations are analyzed, for which the condition number analysis indicates convergence of the solutions obtained by the recursive scheme.

中文翻译：

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球面几何中的辐射传导传递方程：使用条件数准则分解的算术稳定性

球面几何的 $$S_N$$ 近似中的辐射-传导传输方程使用改进的分解方法求解。这项工作的重点是展示如何在递归方程系统中分配源项，以保证算术稳定性，从而保证所获得解的数值收敛，由条件数准则指导。将一些实例与文献结果进行比较，分析参数组合，条件数分析表明递归方案得到的解是收敛的。