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The dimensionless form of this equation is:

d^2X/dη^2 +φΧ^2=0 with X=Ca/Cao =,η=x/B/2 and φ=B^2kCao/4Da which is second order linear equation

Note: You still need to convert the boundary conditions

b.

What is an appropriate initial guess for this system of equations? Justify your answer.

c.

Solve this system as defined in problem 2.B.3 for:

B = 2 k = 2

CAo = HA*PA = 1

DA = 1, 0.1 0.01

N = 100

(Note: 3 different values of DA= 3 different solutions)

Use of analytical Jacobian is not required for this part.

d.

Solve this problem using the Newton and Broyden methods for various number of grid points for DA = 0.1. Plot the solution (only for Newton), computational time (use tic/toc), number of iterations, and number of function evaluations per each N in:

N = [10 50 100 200 400 600 800]';

e.

Derive the Jacobian for the system to speed up the calculations. Solve this problem using the Newton and Broyden methods for various number of grid points for DA = 0.1 with and without the analytical Jacobian (can also add the Jacobian being sparse). Plot the solution (only for Newton), computational time (use tic/toc), number of iterations, and number of function evaluations per each N in:

N = [10 50 100 250 500 750 1000 1500]'

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# Matlab help

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