CONVECTIVE DiffusION WiTH REACTION

solve using matlab

$1)$Discretizing the differential equation

$2)$Simplify to the form Ax $=$ b

$3)$ Matlab solution for x

Consider a tubular vessel where a mixture of two species $($A and B$)$ is flowing in the axial $(x)$ direction. Both species are transported by convection and diffusion. In addition, a first$-$order chemical reaction $A{?}^{k}B$ is taking place in the vessel. $($Such a vessel is called a tubular reactor.$)$ The relevant differential equation $($species balance$)$ that describes the concentration variation of $A$ in the vessel at steady state is$,$

$D\frac{d^2{C}_A}{d{x}^2}-u\frac{d{C}_A}{dx}-k{C}_A=0$

The boundary conditions are

@$x=0,u{C}_{A,in}=u{C}_A-D\frac{d{C}_A}{dx}$;$>x=L_{,}\frac{d{C}_A}{dx}=0$

Obtain the general solution for the differential equation, assuming $=($it $(u^2-4kD)>0.$ Obtain the particular solution.