function demo4_1
% demo for the accuracy of the two point finite differencies.
x=[-1:0.1:1];
%% h=0.01 
h=0.01;
figure(1)
subplot(2,3,1);
plot(x,f_der(x),'-r');
hold on;
plot(x,(f(x+h)-f(x))/h,'-b'); % forward difference
plot(x,(f(x+h)-f(x-h))/(2*h),'-g'); % central difference
hold off
%% h=0.00001 
h=0.00001;
figure(1)
subplot(2,3,2);
plot(x,f_der(x),'-r');
hold on; 
plot(x,(f(x+h)-f(x))/h,'-b'); % forward difference
plot(x,(f(x+h)-f(x-h))/(2*h),'-g'); % central difference
hold off
%% h=0.000001 
h=0.000000000000001;
figure(1)
subplot(2,3,3);
plot(x,f_der(x),'-r');
hold on;
plot(x,(f(x+h)-f(x))/h,'-b'); % forward difference
plot(x,(f(x+h)-f(x-h))/(2*h),'-g'); % central difference
hold off
%%%%%%%%%%%%%%%%%%%%%%%%
h=0.01;
figure(1)
subplot(2,3,4);
plot(x,f_der(x)-(f(x+h)-f(x))/h,'-b'); % forward difference
hold on;
plot(x,f_der(x)-(f(x+h)-f(x-h))/(2*h),'-g'); % central difference
hold off
%% h=0.00001 
h=0.00001;
figure(1)
subplot(2,3,5);
plot(x,f_der(x)-(f(x+h)-f(x))/h,'-b'); % forward difference
hold on;
plot(x,f_der(x)-(f(x+h)-f(x-h))/(2*h),'-g'); % central difference
hold off
%% h=0.000001 
h=0.000000000000001;
figure(1)
subplot(2,3,6);
plot(x,f_der(x)-(f(x+h)-f(x))/h,'-b'); % forward difference
hold on;
plot(x,f_der(x)-(f(x+h)-f(x-h))/(2*h),'-g'); % central difference
hold off

function y=f(x)
y=x.^2;

function y=f_der(x)
y=2.*x;