Point Kinetics Equation with $6$ Delayed Groups

Task

Describe the physical meanings of the point kinetics equations and the parameters in the equations.

Ex$)$ Prompt neutron, delayed neutron, fission product, beta decay, neutron life time, $$ and $\backslash$lambda $,$ etc.

Write a Python program to solve this problem using the $4$th order Runge$-$Kutta method and obtain the reference solution up to $1$ sec with At $=0\mathrm{.}0001$ s$.$

Write a subprogram for the explicit and modified Euler methods, respectively. Solve the problem with At $=0\mathrm{.}02,0\mathrm{.}01,0\mathrm{.}005,0\mathrm{.}001($sec$)$ with explicit, modified Euler's and $4$th order RK methods.

$.$ Plot the solution and examine the dependence of the error in the peak power and time on the time step size.

Discussion