Project #16926 - numerical analysis

Write down the system of nonlinear equations that must be solved in order to apply the backward Euler method to the following system of ODE:

R′ = (2 - F)R

F′ = (R - 2)F

, starting with R0 = 2 and F0 = 1 and using step size Δt = 0:1.

 I decoupled and I get 2FR -(RF^2)(.5) = (FR^2)(.5) - 2FR +C. I think next I would plug in initial values for R and F, and solve for C.. and then?

I understand the below newtons part, the above part is my quandary.

With an initial guess of R(0)1 = 2

and F(0)1 = 1, write down one step of Newton's method that would be taken to solve for R1 and F1.

 

need explanation of reasoning

Subject Mathematics
Due By (Pacific Time) 11/15/2013 12:00 am
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