Chapter 11, Problem 27P

As described in Sec. PT3.1.2, linear algebraic equations can arise in the solution of differential equations. For example, the following differential equation results from as tea dy-state massbalance for a chemical in a one-dimensional canal,

$0=D\frac{d^{2}c}{d{x}^2}-U\frac{dc}{dx}-kc$

Where $c=$ concentration, $t=\text{time, }x=\text{ distance, }D=$ diffusion coefficient, $U=$ fluid velocity, and $k=\text{a}$ first-order decay rate. Convert this differential equation to an equivalent system of simultaneous algebraic equations. Given $D=2,U=1,k=0.2,c\left(0\right)=80\text{ and }c\left(10\right)=20$, solve these equations from $x=0\text{ to 10 with }\Delta x=2$, and develop a plot of concentration versus distance.