Need Help with Solving Point Kinetic Equation for One group

[Sherin]

Does anybody can help solve point kinetic equation for one group of delayed neutrons in steps. I am looking forward to solve it by analytical methods.

dn(t)/dt=ρ-β/l n(t)+ λC(t)

dC(t)/dt= βi* n(t)/l- λC

I would really appreciate your help as i am have to submit to clear this paper next week

 

[Astronuc]

Well, one has two coupled first order differential equations, and they seem to have constant coefficients.

What are the initial conditions? One could try substitution.

How about demonstrating some effort and showing one's work?

 

[Sherin]

dn(t)/dt=ρ-β/l n(t)+ λC(t) ----------------------------------(1)

The Taylor series expansion of the neutron density can be written as follows and also
we can write an expression that can be used to find the

neutron density at a later time from the neutron density at the earlier time

N(t+h) = N(t)+ h *dN/dt +1/2! * H^2*d^2N/dt^2

BUT THE SOLUTION SAYS
Compute the right-hand side of the point kinetics equations (Eq. (1) using the neutron density concentrations from the previous time step. Then multiply the result by the time-step size h.

I would like to know how to perform this step. Kindly help me.

 

[DrJHBickel]

Maybe it would be easier to try solving case of a simple step change. That can be demonstrated with pencil and paper.