CONSTRUCTING A SCHEME TO SOLVE THE NUCLEI KINETICS PROBLEM
D. G. Modestov
VANT. Ser.: Mat. Mod. Fiz. Proc 2018. Вып.4. С. 19-28.
The nuclei kinetics problem is the Cauchy problem for a system of differential equations in which the right-hand sides, in a simplest case, are the functional on the transport equation solution. The resultant equation system is rigid. It is usually solved with the specialized methods using the behavior specifics of the given system physical characteristics. A most common approach is the use of the first-order scheme, although it seems a higher order of accuracy could allow reducing the labor input. However, the analysis has demonstrated that, in general, the construction of scheme above the second order of accuracy is impossible. Results of simulations for a methodological problem are presented as an example and they demonstrate that even such schemes allow significantly decreasing the amount of calculations for solving problems, which are not too extremal. Keywords: nuclei kinetics, numerical schemes, Cauchy problem, an integration scheme, the particle transport equation, the method of generations.
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