Numerical solution of the chain model of fission product nuclides. Effect on the reactivity of the reactor

Runge–Kutta algorithm of fourth order devised for the numerical solution of ordinary differential equations of fuel isotopic composition and fission products accumulation systems is described. Several hundreds fission product isotopes are included in partially depleted fuel as a result of direct yield from nuclear fission reaction, radioactive decay of fission products and/or neutron capture. The algorithm of the suggested method was coded and compared with both the analytical method and the international ORIGEN2 code system. The accuracy and speed of the calculations as obtained by implementing the method in a PCs with Linux system are found to be acceptable and faster than their resemblance. The effect of the calculated fission product concentrations on the reactivity of the reactor has been included.