Abstract

We study numerical solution of Singular Integral Equations (SIE) of particle transport theory. We convert them into matrix equations by standard discretization process. It is found that the matrices are highly ill-conditioned and can be solved by Singular Value Decomposition (SVD) method. One expects that matrices resulting from expansions over Partial Range will not be ill-conditioned. We find this is not true though their ill-conditioning is an order of magnitude less than those of full or half range. Reasons for this phenomenon are explained.

中文翻译：

---

案例特征函数的局部范围完备性和粒子输运问题的奇异积分方程的数值解

摘要

我们研究粒子传输理论的奇异积分方程（SIE）的数值解。我们通过标准离散化过程将它们转换为矩阵方程。发现矩阵的病态严重，可以通过奇异值分解（SVD）方法求解。人们期望，由部分范围内的扩展产生的矩阵不会病态。我们发现这是不正确的，尽管他们的病态比全范围或一半范围的病态小一个数量级。解释了这种现象的原因。