# runge: The Runge phenomenon for polynomial interpolation
# wild oscillations for large degree polynomials.

runge := proc(n)
   # n is the degree of the polynomial
   local f, xp, yp, i, poly, p1, p2, caption;
   f := x -> 1 / (1+x^2);
   xp := [ seq(-5+i*10/n, i=0..n) ];
   yp := map(f,xp);
   poly := interp(xp,yp,x);
   caption := cat(`degree = `, n);
   p1 := plot(f(x), x=-5..5, y=-2..2, numpoints=401);
   p2 := plot(poly, x=-5..5, y=-2..2, numpoints=401, color=red);
   plots[display]([p1,p2], title=caption);
end:

# f is an even function so we should use even degree polynomials

for n in [2,4,10,20,50,100] do
   interface(plotdevice=gif, plotoutput=`runge`.n.`.gif`);
   runge(n);
od;