INTEGRATING THE NUCLEAR COMPOSITION EVOLUTION EQUATIONS OF MATERIALS IN STATIC RADIATION FIELDS
D. G. Modestov
VANT. Ser.: Mat. Mod. Fiz. Proc 2012. Вып.1. С. 17-28.
It is impossible to use precision methods for some problems. This is true, in particular, for nonlinear problems associated with finding the parameters of material exposed to radiation. Though approximations, which consist in dividing a time interval into sections of a constant radiation density, are permitted for such problems, the resultant set of linearized problems also has no exact solution, in general case.To find approximate solutions to such problems, a set of schemes of different orders of accuracy based on representing a linear operator as a sum of two operators is proposed. One of them has a high norm, however, it admits an exact solution. The second one having a low norm is considered to be a small add-in. With such approach it is possible to estimate the obtained solution accuracy, or estimate the numerical integration step required to provide the given accuracy. The correspondence of the estimated accuracy and error is considered by the example of methodological problems. Keywords: nuclear composition, isotope composition, reactor, burnup, decay, reaction cross-section, Cauchy problem, numerical methods, integration scheme, order of accuracy, estimation of errors.
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