Problem 2

The following steady-state transport model is to be used to determine the concentration profile

of a proppant in a fracturing operation:

(a) Set up the numerical solution to solve this problem using explicit finite-difference with a

step size of 1 m. Set up the solution matrix, and state how you would solve it to obtain

the concentration profile over the full range 0 ≤ x ≤ 100m.

What error order would you expect, and how can you improve quality of your solution?

Write a Matlab program to solve the above system of ODEs using the explicit finite-

difference method in the interval: [x = 0 to x=100]. Investigate the effect of step size on

the solution.