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 a steady-state mass balance for a chemical in a one-dimensional canal,

Where c = concentration, t=time, x=distance, D=diffusion coefficient, U=fluid velocity, and k=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(0)=80 and c(10)=20, solve these equations from x=0 to 10 with (x=2, and develop a plot of concentration versus distance?

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dckc dud