Abstract

In recent years, the first author has developed three successful numerical methods to solve the 1D radiative transport equation yielding highly precise benchmarks. The second author has shown a keen interest in novel solution methodologies and an ability for their implementation. Here, we combine talents to generate yet another high precision solution, the Matrix Riccati Equation Method (MREM). MREM features the solution to two of the four matrix Riccati ODEs that arise from the interaction principle of particle transport. Through interaction coefficients, the interaction principle describes how particles reflect from- and transmit through- a single slab. On combination with Taylor series and doubling, a high-quality numerical benchmark, to nearly seven places, is established.

摘要

近年来，第一作者开发了三种成功的数值方法来求解一维辐射输运方程，产生高精度基准。第二作者对新颖的解决方案方法和实施能力表现出浓厚的兴趣。在这里，我们集思广益，生成了另一种高精度解决方案，即矩阵 Riccati 方程方法 (MREM)。MREM 具有四个矩阵 Riccati ODE 中两个的解，这些矩阵由粒子传输的相互作用原理产生。通过相互作用系数，相互作用原理描述了粒子如何从单个平板反射和透射。结合泰勒级数和倍增，建立了一个高质量的数值基准，达到近七位。