Problem with plotting a function in MATLAB

[diredragon]

Homework Statement

Write code for solving the integral $\int_{0}^{x}e^{-t^2}dx$ using simpsons method and then plot the function from $x = 0$ to $x = 5$ with $0.1$ increment.

Homework Equations

3. The Attempt at a Solution [/B]
I was told that the best way to plot the function is to write it in Matlab so i decided to give it a go since i haven't really worked in MATLAB before.This is my integral solution code:

function y = simpson_method(x)

y1 = exp(-0.^2);
y2 = exp(-(x).^2);

c = 0;
d = 0;
incr = 0.1;

for i = 1 : (x - 0)/incr - 0.5

   
    y = exp(-(0 + i*incr).^2);

   
    if i/2 == floor(i/2)
       
        d = d + y;
        continue
    else
        c = c + y;
        continue
    end
end

y = incr/3 * (y1 + 4*c + 2*d + y2);

and the plot code:

x = 0:0.1:15;
y = simpson_method(x);
plot(x,y)

But the output plot is wrong and looks like this:

Which is weird since the function i wrote gives correct values at all points. What is wrong here?

 

[Orodruin]

You might want to check whether or not your function gives the correct output when you feed it a vector of several points to evaluate it at.

 

[diredragon]

You might want to check whether or not your function gives the correct output when you feed it a vector of several points to evaluate it at.

I'm not sure how to do that on MATLAB just yet. Is there somewhere i can see examples of that?

 

[Orodruin]

That is what you are doing when you first write x = 0:9.1:15 and then function(x). You are passing a vector as argument and your function needs to be able to handle that.

 

[diredragon]

That is what you are doing when you first write x = 0:9.1:15 and then function(x). You are passing a vector as argument and your function needs to be able to handle that.

It does output wrong when i input a vector. How do i fix that in the code? How to make a function able to handle a vector?

 

[FactChecker]

You should take a close look at your function. Notice that y1 is always 1. Is that what you want in the last equation for y? I recommend that you simplify the function, add comments to keep it clear, and do not use the variable y inside the loop.

 

[diredragon]

You should take a close look at your function. Notice that y1 is always 1. Is that what you want in the last equation for y? I recommend that you simplify the function, add comments to keep it clear, and do not use the variable y inside the loop.

I made all the corrections and it's still outputting wrong when i feed it a vector like before.

function y = simpson_method(x)  %function which i integrate is e^(-x^2)
 yn = exp(-(x).^2);                    %I am using the simpsons method which calculates like this:
                                             %h/3*(f(0) + 4*(f1) + 2*(f(2) + 4*f(3) + ... + f(n))
c = 0;
d = 0;
h= 0.1;

for i = 1 : (x - 0)/h - 0.5                 %summing the parts of the function

  
    f = exp(-(0 + i*h).^2);                %calculating f(i*h)

  
    if i/2 == floor(i/2)                   %checking whether it's even or odd i and adding it to the sum
      
        d = d + f;
        continue
    else
        c = c + f;
        continue
    end
end

y = h3 * (1+ 4*c + 2*d + yn);         %summing all the parts and return the integral

It has to be that it can't handle a vector but I am not sure how to fix that.

 

[Orodruin]

for i = 1 : (x - 0)/h - 0.5 %summing the parts of the function

What do you think this line does?

Edit: I also strongly advice against using i as a variable. It should be reserved for the imaginary unit.

 

[diredragon]

What do you think this line does?

This line is a for loop which increases i from 1 to x/n which is a number of sub-intervals. The -0.5 was added as it does not output correct when i simply write x/n

 

[Orodruin]

But the x you input is a vector!

 

[diredragon]

But the x you input is a vector!

Oh i see it now, can't use x. Does it also pose a problem in the definition of yn? Also do i now need somehow to state that only one element at a time from x is used in the loop. How do i do that?