# Six group point kinetic equation

1. May 18, 2007

### caldus2311

Hello.

I would be very thankful with some help with the numerical solution of the six group point kinetic equations, with the constant reactivity (step change).

I would like to do this with the Mathematica.

Thanks.

Best regards, Dusan

2. May 20, 2007

### caldus2311

Does anyone have any experience with numerical solution of the 6 group point kinetic equation, with the step reactivity change?

Anyone?

Thanks.

3. May 21, 2007

### Astronuc

Staff Emeritus
Dose the solution involve one-group diffusion with 6 delayed groups, so that one is solving the one group neutron diffusion equation and 6 equations for each group of precursors? Presumably the reactivity is between 0 and beta?

I've solved the inhour equation and one group w/ one delyed, but that was 25 years ago, so I may be slow on this.

What equations are you using?

4. May 21, 2007

### caldus2311

Hello.

I am trying to solve the following 7 equations:
dn(t)/dt=ρ-β/l n(t)+∑6i=1 λiCi+Q0/l

dCi(t)/dt= βi* n(t)/l- λiCi.

Where Q0 is constant extra source with neutrons per second.

Lets say that I have the subcritical reactor with the reactivity ρ=-0.0526, which corresponds to k=0,95 (multiplication factor).

Now I increase the reactivity to ρ=-0.04167 (step reactivity change), which corresponds to k=0,96.

What is the n(t) in 6 group approximation.

I already made the analytical solution with one group approximation and now I am trying to find the numerical six group solution. Most probably I will do this with Runge-Kutta method. I just wanted to ask if there is someone with any experiences?

Thanks

5. May 21, 2007

### Astronuc

Staff Emeritus
Runge-Kutta is the standard approach to solving these couple diff EQs.