Chapter 8.4, Problem 3CP

Solve Fisher’s equation (8.69) with $D=1,f(u)=u(u-1)(2-u)$ and homogeneous Neumann boundary conditions, using initial condition (a) $f(x)=1/2+\cos 2\pi x$, (b) $f(x)=3/2-\cos 2\pi x$ . Equations (8.71) and (8.72) must be redone for the new $f(u)$. Plot the approximate solution for $0\le t\le 2$ for step sizes $h=k=0.05$

. Which equilibrium solution does the solution approach as time increases? What effect does changing D to 0.1 or 0.01 have on the behavior of the solution?