An improved reproducing Hilbert kernel method to solve the model of neutron transporting process in nuclear reactor core

We propose an adaptive double piecewise interpolation reproducing Hilbert kernel method (ADPIRHKM) for the first time to solve the model of the neutron transporting process in the nuclear reactor core. The theory focuses on the reproducing kernel theory, integrated with the adaptive technique and the double piecewise interpolation means, which can produce a sparse matrix B by selecting the appropriate parameters, avoiding calculating the conjugate operator and practising Gram-Schmidt orthogonalization. The adaptive multi-step technique, which ensures a more reasonable segment count, and the double piecewise interpolation approach, which enhances accuracy, combine together to give a key innovation point of this paper: a simple and efficient numerical method. Three numerical experiments are done to show the accuracy of the new method and the comparisons are based on the known results. The numerical simulation indicates the effect of time t and \beta on neutron flux behavior of graphite.