Backward euler discretization

1. What is the backward Euler method?
2. Why is backward Euler better than forward?
3. How do you discretize a differential equation?

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 than forward?

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.

How do you discretize a differential equation?

The simplest approach to discretize a differential equation replaces differential quotients by quotients of finite differences. For the space variables this method works best on a regular grid.