Recursive Method returning answers backwards

Consider my code for Euler's Method below. If you run the code, you will see the correct values be stored in the matrix "vals", but after the return statement, the "vals" that is returned is from the first iteration. Why does MATLAB do this?

f = @(x,y)(x^2*(2+y));

ans = euler(1, 0.1, f, 0.0, 1.0, [])

function vals = euler(y,h,f,start,finish,vals)
    if (finish - h < start)
        y;
        return
    else
        y = y + h*f(start,y)
        start = start + h
        vals = [vals,y]
        euler(y,h,f,start,finish, vals)
    end
end

[John D'Errico]

MATLAB does what you tell it to do. It is not DOING anything to you. Just your code, code written in error. Why you are usign recursion, I don't know, since Euler is simple to write with a loop. Read the answer from James.

Answer 1

[James Tursa]

This is a very convoluted way to program the Euler method. There is no need for recursion here, just use simple loops instead.

Regarding why you aren't getting the results you expected, it has to do with how you update vals. Your very first call to Euler is this:

ans = euler(1, 0.1, f, 0.0, 1.0, [])

which returns the vals from the very first call via this line:

vals = [vals,y]

but then in all your subsequent calls to euler( ) you throw away the returned vals:

% you don't save the returned vals, so this line essentially accomplishes nothing
euler(y,h,f,start,finish, vals) 

Maybe changing this euler( ) call to this might get you what you expected:

vals = euler(y,h,f,start,finish, vals)

But, seriously, this code is convoluted and hard to follow because of the recursion. It would be best to rewrite it as a simple loop.

[Chas]

I already had done it with a loop and was curious to figure out how recursion worked in MATLAB. What is a fix to this code? I can't think of one based on your explination.

[Torsten]

Didn't you read to use

vals = euler(y,h,f,start,finish, vals)

instead of

euler(y,h,f,start,finish, vals) 

in your code ?