平板中一维中子输运方程的Lagrange插值数值解
numerical caseology by Lagrange interpolation for the 1D neutron transport equation in a slab
摘要：
在这里，我们关注的是一个新的，高精度的，数值解的基础上的情况下解析奇异本征函数展开（SEE）的一维中子输运方程。虽然目前存在相当数量的数值解，但可以理解的是，由于其复杂性，即使在一维中，中子输运方程也只有少数真正的解析解。1960年，凯斯为各种理想化的运输问题引入了SEE的一致性理论，并永远改变了分析运输理论的面貌。包括FN方法在内的几种数值方法都是基于该理论。提出的是另一种称为Lagrange阶N方法（LNM）的方法，其特点是具有FN方法的简单性和精度，但更方便和自然的Lagrange多项式基。
英文摘要：
Here, we are concerned with a new, highly precise, numerical solution to the 1D neutron transport equation based on Cases analytical singular eigenfunction expansion (SEE). While a considerable number numerical solutions currently exist, understandably, because of its complexity, even in 1D, there are only a few truly analytical solutions to the neutron transport equation. In 1960, Case introduced a consistent theory of the SEE for a variety of idealized transport problems and forever changed the landscape of analytical transport theory. Several numerical methods including the FN method were based on the theory. What is presented is yet another, called the Lagrange order N method (LNM), featuring the simplicity and precision of the FN method, but for a more convenient and natural Lagrangian polynomial basis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
