Matlab Script Accuracy of Results

I'm trying to write a Matlab script that shows the order of accuracy of the forward and central differencing methods for the first derivative of f = exp (x) at x = 0. The graph attached is the result I'm looking for.

Here is what I have so far in forward differencing method but I'm kinda stuck. Can you show me where I made my mistakes.

clear all

close all

delx = 1;

x = 0;

y = exp(x);

fig = figure();

set(fig,'color','white')

plot(x,y,'LineWidth',2)

xlabel('x')

ylabel('y')

grid on

yderiv = exp(x);

fig = figure();

set(fig,'color','white')

plot(x,yderiv,'LineWidth',2)

xlabel('x')

ylabel('y')

grid on

%%%Forward Differencing

yderivest = (y(2:end) - y(1:end-1))./delx;

hold on

plot(x(2:end)-delx/2,yderivest,'r-','LineWidth',2)

Answer 1

[John D'Errico]

You made a LOT of mistakes.

delx = 1;
x = 0;
y = exp(x);

So you set x to zero. Then you evaluated exp(x).

That does NOT create a function of x. It simply evaluates exp(x), thus, here exp(0).

And I'm not sure what you think you are doing here:

yderivest = (y(2:end) - y(1:end-1))./delx;

y is a scalar variable. It is not a vector as you built it.

I'll give you a couple of suggestions to get you started.

Generate a vector of h values. Something like this:

h = 2.^(-20:1:0);

And you might create a function.

testfun = @(x) exp(x);

Now your code will work for other functions, doing not much more than changing testfun.

So what would this do?

x0 = 0;
fdiff = (testfun(x0 + h) - testfun(x0))./h

How would you change that for a central difference?

What is the error in the derivative approximation? Well, you know that the correct derivative is just:

truederiv = exp(x0);
fdifferr = abs(truederiv - fdiff);

Now you can plot the result as a function of h. Plot will work, but perhaps loglog will be a better choice of plotting tool. Think about why that might be true. What does the slope of such a resulting error plot mean when you plot it using loglog axes?

[jcn2912]

How do I plot the result as a function of h? I'm not getting the answer I'm looking for.