IndexError: index 1 is out of bounds for axis 0 with size 1/ForwardEuler

The problem, as the Traceback says, comes from the line x[i+1] = x[i] + ( t[i+1] - t[i] ) * f( x[i], t[i] ). Let’s replace it in its context:

• x is an array equal to [x0 * n], so its length is 1
• you’re iterating from 0 to n-2 (n doesn’t matter here), and i is the index. In the beginning, everything is ok (here there’s no beginning apparently… 🙁 ), but as soon as i + 1 >= len(x) <=> i >= 0, the element x[i+1] doesn’t exist. Here, this element doesn’t exist since the beginning of the for loop.

To solve this, you must replace x[i+1] = x[i] + ( t[i+1] - t[i] ) * f( x[i], t[i] ) by x.append(x[i] + ( t[i+1] - t[i] ) * f( x[i], t[i] ))