When pproximating derivatives at boundaries should the finite differencing be of at least the same order of accuracy as those used in interior points?

Shuo

Hi You don't have to... Most papers uses first or second order approx. at the boundaries, but if you can do it, meaning use the same order, so it's of course better, specially if you're developping a high-order scheme.

It's also important to keep in mind the type of error (dipersive or dissipative), so somethimes it's better to use an inferiror order because its error is dissipative.

Hope it helps

The most important issue to be thought over is the stability of your system when using the same order of approximation which might involve a wider stencil. There is a paper by Carpenter(I do not remember the name ?) which discusses this issue in detail. There are many numerical schemes which use the same order of accuracy at the boundary/interior.