Euler method for ODE

I wrote the following code for Euler method

function sol=Euler2(fn,a,b,y0,n)
h=(b-a)/n;
x=a:h:b;
y(1)=y0;
for k=1:n 
    y(k+1)=y(k)+h*feval(fn,x(k),y(k));
end
sol=[x',y'];

Suggest me to obtain 'y' vector without 'for' loop, i.e., vectorising statement which can replace the 'for' loop

Answer 1

[James Tursa]

In general, you can't "vectorize" this process as you suggest. Since the calculation for y(k+1) depends on y(k), the calculation must be done in a loop as you are currently doing. An exception would be in cases where the fn function was of a form where the entire result could be obtained analytically (e.g., fn was a constant). But for your case, where fn is some arbitrary function being passed in, you cannot do that and as a result you will need the loop.