Euler's Method

I'm getting an error that reads "Error in myeuler (line 22)

y(i+1) = y(i) + (dx * f(x(i),y(i)));"

I don't exactly know what I'm doing wrong or even where to look in this line to see what's wrong.

% must call from edrive.m or other
% required input arguments: RHS function of two variables f, 
%                           vector x of length n+1, 
%                           init val c
% computed output argument: y\in\R^{n+1} approximate solution

function y = myeuler(f,x,c)

% approximates sol to y' = f(x,y) over [a,b] with y(a)=c
% via n steps of Euler's method

for n = [10, 20, 40, 80, 160]
    a = 0; b = .5; c = .25;
    x = [a:n+1:b];
    f = @(x,y) (x.^3);    

    
dx  = (x(end)-x(1))/n; 
y   = [c ; zeros(n,1)]; 

for i = 1: n
    y(i+1) = y(i) + (dx * f(x(i),y(i)));
end

end

[Image Analyst]

You forgot to give us the actual error. That means ALL the red text, not just a small snippet of it. By the way, your f does not seem to use y at all:

f = @(x,y) (x.^3);

You can see that it just returns x cubed. The y value is ignored.

[Mikela Petersen]

the error is the first thing that was listed:

>> myeuler

Index exceeds the number of array elements (1).

Error in myeuler (line 22)

y(i+1) = y(i) + (dx * f(x(i),y(i)));

Answer 1

[Walter Roberson]

for n = [10, 20, 40, 80, 160]
    a = 0; b = .5; c = .25;
    x = [a:n+1:b];

Consider the first case, n = 10 . Then

    a = 0; b = .5; c = .25;
    x = [0:10+1:.5]
    

but 0:11:.5 is going to give you just 0 .

The number in the middle in a a:b:c operation is the increment, not the number of elements to generate. To generate a particular number of elements,

    x = linspace(a, b, n+1);

Answer 2

[Rafael Hernandez-Walls]

for n = [10, 20, 40, 80, 160]
    a = 0; b = .5; c = .25;
    x = linspace(a,b,n);%[a:n+1:b];
    f = x.^3;    
    dx  = x(2)-x(1);%(x(end)-x(1))/n; 
    y   = [c ; zeros(n-1,1)]; 
for i = 1: n-1
    y(i+1) = y(i) + dx * f(i);
end
plot(x,y),hold on
end