We consider in this contribution a simplified idealized one-dimensional model in a nuclear core reactor coupling the diffusion equation on the neutron flux withthe enthalpy equation for the water which collects the heat produced by this idealized nuclear core. These equations are coupled through the dependency of thecoefficients of the diffusion equation in terms of the enthalpy. We propose a numerical method treating globally the coupled problem for finding its unique solution.Simultaneously, we use incomplete elliptic integrals to represent analytically the density of neutrons and the enthalpy in the fluid. Both methods lead to the samesolution with high accuracy. However, another quantity, generally used as a benchmark for comparing results, depends considerably on the approximation used forthe coefficients of the diffusion equation.

翻译：本文考虑核反应堆堆芯中一个简化的一维理想化模型，该模型将中子通量的扩散方程与收集理想化堆芯产生热量的水焓方程相耦合。这些方程通过扩散方程系数对焓值的依赖关系实现耦合。我们提出了一种全局处理耦合问题的数值方法，用于寻找其唯一解。同时，我们利用不完全椭圆积分解析地表示流体中的中子密度与焓值。两种方法均能以高精度得到相同解。然而，另一个通常用作结果比较基准的量，其计算结果显著依赖于扩散方程系数所采用的近似方式。