Backward euler method pdf

1. What is the backward Euler method?
2. Why is backward Euler better?
3. Is backward Euler first order accurate?

What is the backward Euler 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.

Why is backward Euler better?

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.

Is backward Euler first order accurate?

Both forward and backward Euler are first order accurate, meaning that the error in both discretizations is O(∆t).