Determine the solution for the pure diffusion problem, ) = 0, for a one-dimensional material that has a variable conductivity, k=k, + at. the material has a constant area, a, and is of length x=l. this problem is non-linear as the conductivity is dependent on the temperature and must be solved iteratively. 1. for a local volume, find the exact integral form of the governing equation. 2. apply the linear approximation for an internal cell surrounded by two neighbours. 3. for this problem, the essential boundary condition (also known as dirichlet condition) is imposed at x = 0 and x=l. determine the appropriate approximation formulae for the boundary nodes. 4. solve the problem for l=0.5, t(x=0)=100, t(x=l) = 500, k, = 1000, a = 10 using 100 cells. to solve, you need to modify the code and here is the suggested algorithm, a. input data b. initialize temperature in the domain using the linear solution, t(x)= t(0)+- t(l)-t(0) l and call the solution t_1, then evaluate the conductivity k=k, +at_1 accordingly c. start outer iteration loop (you can set it to 50 iterations) i. evaluate the coefficients ag, ap, ay. b, for boundary cell at x = 0 and fill in first row in matrix ii. evaluate the coefficient az, ap, aw. b, for interior cells and fill in the rows 2 → n-1 iii. evaluate the coefficients ag, ap, aw, b, for boundary cell at x=l and fill in last row in matrix iv. solve to determine the temperature distribution, call the solution t_2 v. evaluate the difference (residual) t_2-t_1 and evaluate the norm. save the norm at each iteration vi. rename the solution t_2 as t_1 vii. evaluate the conductivity k=k, +at_1 and repeat from (1) d. plot the final solution t(x) and the euclidean norm of the residual