% p32.m - solve u_xx = exp(4x), u(-1)=0, u(1)=1 (compare p13.m)

  N = 16;
  [D,x] = cheb(N);
  D2 = D^2;
  D2 = D2(2:N,2:N);
  f = exp(4*x(2:N));           
  u = D2\f;       
  u = [0;u;0] + (x+1)/2;              
  clf
  subplot('position',[.1 .4 .8 .5])
  plot(x,u,'.','markersize',16)
  xx = -1:.01:1;
  uu = polyval(polyfit(x,u,N),xx);
  line(xx,uu), grid on
  exact = (exp(4*xx) - sinh(4)*xx - cosh(4))/16 + (xx+1)/2;
  title(['max err = ' num2str(norm(uu-exact,inf))],'fontsize',12)