unsure on index notation

hiya! im currently working on some tutorial stuff for my degree and am tasked with creating some code to run a forward euler method. A lecturer last year used this

for j = 0:2
    i = i + 1 
    blah
end
 

and it works but i dont really understand why. can someone explain? heres the code im using in full. Im still new to code so be gentle T_T

hold on
h = 0.1;
t = 0: h: 1;
i = 0;

f=@(x)((t.^2)./cos(x)); 
a=1; b=-2; 
tol=1e-4;
c=(a+b)/2;
brack(f,a,b,tol); %using bracketing method to find step 1
x(1) = c;

for j = 0 : h : 1
    i = i + 1;
    t(i+1) = t(i) + h;
    %forward euler for (i+1)
    xfe = x(i) + h.*((t(i).^2)./cos(x(i)));
    %then backwards
    x(i+1) = x(i) + h.*((t(i+1).^2)./cos(xfe));
end
plot(t,x)

[Image Analyst]

Try adding a comment before every single line and be as descriptive as you can. Often when you explain it to somebody, you understand it better yourself.

Answer 1

[Ravi]

Hi Charlie,

I assume you are facing trouble understanding the different uses of the for-loop indexing. The first one uses a: b notation, and the second one uses a: step: b notation.

for j = 0:2
    i = i + 1
    blah
end

In this case “j” takes only integers starting from 0 and ending at 2. That is, the code section in the loop executes for “j” values 0, 1, and 2.

for j = 0:h:1
    i = i + 1;
end

In this case, “j” is not restricted to take only integer values. Instead, “j” starts at “a” and is incremented by “step” every time until the value of j does not exceed “b”.

Hope this helps you understand the indexing better.

Thanks,

Ravi Chandra