I have been given some problems to work through regarding truncation errors of self adjoint boundary value problems. A standard difference scheme is used and then the values are Taylor expanded.

How do you know how many terms to expand about?

For one variable he goes up to four terms with O(h^5) and the other with only three terms with O(h^4) with no reason for doing so.

Also in the expansion of some terms multiplied together he discards terms of order greater than 5. i.e. all the terms with h^6, h^7...

Is there a reason for this.

Is there a certain rule that I'm missing?

Any help will be greatly appreciated