Solution of the Equations of Nuclide Kinetics

Many methods and computational programs are now available for solving burnup equations. Three fundamentally different approaches are combined in a single control program OpenBPS: solution of the nuclide kinetics equation by expansion of a matrix exponential, an iterative method with the possibility of analyzing uncertainties, and a direct analytical solution. The matrix exponential solution is obtained using the modern Chebyshev rational approximation method CRAM. An iterative method taking into account the errors of the initial data and data on decay and cross sections, made possible by an exponential representation of the increment of the nuclide concentration at the BPSE computational step, affords the possibility of analyzing the uncertainty of the nuclear concentration. An analytical computational method based on the use of modified Bateman functions, which is the basis of the ASBE computational code, was developed for the accelerated solution of the burnup equations. Using this program, a solution is obtained more than 100 times faster than the solution speed of programs based on the iterative method with high solution accuracy.