Index exceeds the number of array elements (5)

I am solving Forward Euler for dy=x*y+1, x between 0 and 1, y(0)=0 h=.25

I have gotten the error message "Index exceeds the number of array elements (5)" after rearranging the code (because I was getting other error messages). How can I clear it up?

clc; clear all;
h=0.25; % step size
xmin=0;
xmax=1;
x=xmin:h:xmax; %x boundaries
n=length(x);
y=zeros(1,n);% Initial condition
for i=1:n
x0=0;
dy=(x(i+1)*y(i)+1);
x(i+1)=n*h;
y(i+1)=y(i)+h*dy; 
end
figure(1)
hold on
plot (y,x,'b', 'linewidth',2)
title ('Forward Euler')

[Matt J]

Kolleggerm1's comment moved here:

So I added a line to the for-loop to identify the max of i which seemed to solve the exceeding error, but now I get an error "Array indices must be positive integers or logical values" in line 10

clc; clear all;
h=0.25; % step size
xmin=0;
xmax=1;
x=xmin:h:xmax; %x boundaries
n=length(x);
y=zeros(1,n);% Initial condition
for i=1:n
i=0:1:4;
dy=(x(i+1)*y(i)+1);
x(i+1)=n*h;
y(i+1)=y(i)+h*dy; 
end
figure(1)
hold on
plot (y,x,'b', 'linewidth',2)
title ('Forward Euler')

Answer 1

[the cyclist]

You have initialized x and y to be vectors of length 5. But in your for loop, i reaches the value value 5, and then you try to access x(i+1), which is x(6), which does not exist. You could run your for loop over just i = 1:n-1.

[Kolleggerm1]

Thank you for your response, but when I adjusted to i=1:n-1, my x values all became 1.25 when they aren't supposed to exceed 1 (and are supposed to go up by 0.25).

[the cyclist]

The endpoint of your loop has nothing to do with that. Your values of x are all 1.25 because

x(i+1)=n*h

is always evaluated to 1.25. Maybe you meant

x(i+1)=i*h

?

So, fixing both of those things, you would have

clc; clear all;
h=0.25; % step size
xmin=0;
xmax=1;
x=xmin:h:xmax; %x boundaries
n=length(x);
y=zeros(1,n);% Initial condition
x0=0;
for i=1:n-1
    dy=(x(i+1)*y(i)+1);
    x(i+1)=i*h
    y(i+1)=y(i)+h*dy
end

figure
hold on
plot (y,x,'b', 'linewidth',2)
title ('Forward Euler')

[the cyclist]

Also ... did you intend to plot x on the vertical axis? If not, then

plot(x,y,'b','linewidth',2)

instead.

[Guanyang Liu]

Howdy!

Thanks so much for sharing! I came across this thread as I'm having the same problem.

I tried to add an if-else strucutre in the for-loop: if i ==n, it will not appear i = n + 1, but the error is still there - it seems that before running line-by-line throught the code, MATLAB will first diagnose the index in the code and ignore the if-else structure - is that true?

Thanks again and I'd like to start a new thread if you prefer.

[the cyclist]

I did not fully understand your question.

I think you should open a new one, with your code included.

MATLAB is a procedural language, and always runs through the code in order.

[Guanyang Liu]

Thank you so much for your prompt reply! I'll start a new thread then

Answer 2

[Matt J]

for i=1:n-1