Numerical Methods, please provide detailed solution. Thanks.

Question 2 Answer in a separate book marked Question 2. An insulated heated rod with a uniform heat source x) can be modelled with the Poisson equation 5! 21\" E = 'fl Given a heat source f(x)=25 'Cfmz and the bmmdary conditions H: = 0) = 40 "C, T(x = 10) = 200 \"C (a) Divide the rod into N equal parts and write the nite difference form of the equation above that relates the temperature inside of the rod at node 1', I}, to the temperatures at the neighboring nodes using the central-difference formula. (b) Use N=5 which corresponds to Ax = 2 and write the coefcients A;, Bi, C; and D,- to obtain the system of linear equations for all interior points 4114+Bf11+ci11+l=n i=1,2,...,N1 (c) Express the system of equations in matrix form and discuss which method you would use for solving this system of equations in order to nd the temperature distribution in the rod. You are not required to solve the system of equations