使用中子密度一阶泰劳多项式分段近似技术，给出一个新的求解点堆中子动力学方程组的数值方法并采用全隐格式以克服方程组的刚性，同时确保解的必要精度。数值结果表明：在隐式一阶多项式近似下，对合适的反应性输入能够取得足够精确的结果。当反应性给定时，对于求解反应堆动力学问题，能给出一个简法的计算过程。 Using neutron-density first order Taylor polynomial piecewise approximation technique, a new numerical method for solving point-stack neutron kinetic equations is given and the full implicit scheme is adopted to overcome the rigidity of the system while ensuring the necessary accuracy of the solution. The numerical results show that with an implicit first-order polynomial approximation, sufficiently accurate results can be obtained for the appropriate reactivity input. When reactivity is given, a simplified method of calculation can be given to solve the reactor dynamics problem.