Use finite differences with N nodes to approximate this BVP by a system of algebraic equations. Use the centered difference scheme for the first derivatives. Describe the placement of your nodes and show equations for both interior nodes and nodes which involve the boundary conditions. Clearly indicate the number of equations and unknowns and make sure they are equal

Problem 1 Consider the boundary value problem described in the figure below. In this process, a contaminant is removed from a water stream in the top channel using a membrane. The membrane allows the contaminant to pass through into a fresh stream in the bottom channel, but it is impermeable to water. The top stream is the 'concentrated' stream, which enters with contaminant concentration CC=1, while the bottom stream is the 'dilute' stream, which enters with concentration Cd=0. The streams flow in the same direction with fixed velocities vc and vd. The rate at which the contaminant crosses the membrane depends on the concentration difference and can be expressed as p(CcCd), where p is a constant. The differential equations governing the concentrations on the concentrated and dilute sides of the membrane are as follows, where D is also a constant: Dx22Cc+vcdxdCc=p(CcCd),Dx22Cd+vddxdCd=+p(CcCd) In this problem, you solve this BVP using finite differences with step size h. For your solution, use a mesh with N interior nodes and the boundaries at nodes 0 and N+1. Specifically, 0=x0