Chapter 28, Problem 12P

The following system is a classic example of stiff ODEs that can occur in the solution of chemical reaction kinetics:

$\begin{array}{l}\frac{d{c}_1}{dt}=-0.013c_1-1000c_1{c}_3\\ \frac{d{c}_2}{dt}=-2500c_2{c}_3\\ \frac{d{c}_3}{dt}=-0.013c_1-1000c_1{c}_3-2500c_2{c}_3\end{array}$

Solve these equations from $t=0$ to 50 with initial conditions $c_1\left(0\right)=c_2\left(0\right)=1\text{ and }{c}_3\left(0\right)=0$. If you have access to MATLAB software, use both standard (for example, ode45)and stiff(for example, ode23s) functions to obtain your solutions.