Abstract Point kinetics equations (PKEs) is an significant model used to describe dynamic behaviors of neutron in nuclear reactors. How to cope with its stiffness problems is very important to solve PKEs accurately and efficiently. In this paper, a new semi-analytical algorithm based on Euler-Maclaurin Approximation (SAEMA) is developed to solve PKEs. SAEMA algorithm is applied and tested in different reactors with three typical reactivity insertion cases, including step, ramp and sinusoidal insertions. Firstly, the investigations on the computational stability are performed under different time step sizes. Secondly, the performances on computational accuracy are evaluated by comparing the results by SAEMA algorithm with the ones by analytical method and excellent CATS algorithm. Finally, by comparing the CPU time consumed by SAEMA algorithm with the physical time, the studies on the computational efficiency are also carried out. Just as results shows, SAEMA algorithm is reasonably an attractive way to solve the PKEs.

中文翻译：

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基于 Euler-Maclaurin 近似求解 PKE 的新半解析算法

摘要 点动力学方程(PKEs)是描述核反应堆中子动力学行为的重要模型。如何处理其刚度问题对于准确高效地求解PKE非常重要。在本文中，开发了一种基于 Euler-Maclaurin Approximation (SAEMA) 的新半解析算法来解决 PKE。SAEMA 算法在不同的反应器中应用和测试，具有三种典型的反应性插入情况，包括阶跃、斜坡和正弦插入。首先，在不同的时间步长下进行计算稳定性的研究。其次，通过将SAEMA算法的结果与解析法和优良CATS算法的结果进行比较来评估计算精度的性能。最后，通过比较SAEMA算法消耗的CPU时间与物理时间，还进行了计算效率的研究。正如结果所示，SAEMA 算法是解决 PKE 的合理有吸引力的方法。