Taylor’s series method for solving the nonlinear point kinetics equations

Taylor’s series method for solving the point reactor kinetics equations with multi-group of delayed neutrons in the presence of Newtonian temperature feedback reactivity is applied and programmed by FORTRAN. This system is the couples of the stiff nonlinear ordinary differential equations. This numerical method is based on the different order derivatives of the neutron density, the precursor concentrations of i-group of delayed neutrons and the reactivity. The r th order of derivatives are derived. The stability of Taylor’s series method is discussed. Three sets of applications: step, ramp and temperature feedback reactivities are computed. Taylor’s series method is an accurate computational technique and stable for negative step, negative ramp and temperature feedback reactivities. This method is useful than the traditional methods for solving the nonlinear point kinetics equations.

► Taylor’s series method for nonlinear point kinetics equations is applied. ► The general order of derivatives are derived for this system. ► Stability of Taylor’s series method is studied. ► Taylor’s series method is A-stable for negative reactivity. ► Taylor’s series method is an accurate computational technique.