A numerical solution of point kinetics equations using the Adomian Decomposition Method

Hag-Tae Kim, D. Hong, K. Chong
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引用次数: 2

Abstract

For solutions to point kinetic equations in nuclear dynamics, various analytical methods have been developed. Nevertheless, sometimes complex aspects of problems make it difficult to apply analytical methods to point kinetic equations. In addition, owing to the stiffness and need for small time steps of point kinetic equations, it is hard to obtain accurate results using analytical methods. As an alternative to these problems, the numerical methods can be used for solutions to point kinetics equations instead of analytical methods. In this work, a numerical solution of point kinetic equations using an inherently large sampling interval is proposed and analyzed. To implement this method, we make use of a useful technique called the Adomian Decomposition Method. Finally, in order to showcase the increased performance, the results of the proposed method are compared to exact values.
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用Adomian分解法求解点动力学方程
对于核动力学中点动力学方程的解,已经发展了各种各样的解析方法。然而,有时问题的复杂方面使解析方法难以应用于点动力学方程。此外,由于点动力学方程的刚度和需要较小的时间步长,用解析方法很难得到准确的结果。作为这些问题的一种替代方法,数值方法可以用来解决点动力学方程而不是解析方法。在这项工作中,提出并分析了采用固有大采样间隔的点动力学方程的数值解。为了实现这个方法,我们使用了一种叫做阿多米安分解法的有用技术。最后,为了展示所提高的性能,将所提方法的结果与精确值进行比较。
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