% numerical verification of the finite difference approximation for % derivatives h = 0.1*2.^(0:-1:-5); u = @(x) sin(x); up = @(x) cos(x); x0 = pi/3; E_plus = ( u(x0+h)-u(x0 ) )./h - up(x0); E_minus = ( u(x0 )-u(x0-h) )./h - up(x0); E_centered = ( u(x0+h)-u(x0-h) )./(2*h) - up(x0); loglog(h,abs(E_plus),'-o','linewidth',2); hold on; loglog(h,abs(E_minus),'-*','linewidth',2); loglog(h,abs(E_centered),'-d','linewidth',2); legend('Forward one-sided approx','Backward one-sided approx','Centered approx','location','northwest'); grid on;
