Frequency warping when integrators are replaced with backward-euler and forward-euler integration

1. Why is backward Euler better than forward Euler?
2. Can you go backwards with Euler's method?
3. How do you use the forward Euler method?

Why is backward Euler better than forward Euler?

The advantage of forward Euler is that it gives an explicit update equation, so it is easier to implement in practice. On the other hand, backward Euler requires solving an implicit equation, so it is more expensive, but in general it has greater stability properties.

Can you go backwards with Euler's method?

The backward Euler method is an iterative method which starts at an initial point and walks the solution forward using the iteration yn+1−hf(tn+1,yn+1)=yn.

How do you use the forward Euler method?

To estimate a solution for Forward Euler, you just start with y(t0) and sum up the steps you make with closed eyes, which we can write with summation notation: y(t0+3Δt)≈y(t0)+2∑i=0f(t0+iΔt)Δt.