Hi all,

I am wondering if anyone could tell me why the forward euler time differencing scheme refers to that scheme which uses current values to evaluate the spatial difference( when dealing with an advection equation for example). It would seem more correct to refer to the scheme which uses known values as the backward time differencing scheme. Where have I gone wrong?

It's because of the form of the finite difference:

The backward difference is the one sided differnce from the left (backwards) from the point where you are evaluating the derivative.

Similarly for the forward difference you are differentiating from the right (forward of the point).

Tom is correct. Imagine a point on a curve - point 1.

To find the new point (at new time) using an explicit scheme we take the gradient at point 1 and project it to point 2 - hence a forward projection.

To find the new point (at new time) using an implicit scheme we take the gradient at point 2 and extrapolate it back to point 1 - hence a backwards projection.