CD Derivation - Step 3

[caladoa]

I noticed what I think is a mistake in the derivation for central difference scheme for the 2nd order derivative in Step 3:

It is stated that the 4th order terms are negligible and can be discarded, however this term remains in the next equation. I believe these terms remain until we divide all terms in the equation by dx ^ 2 , thus leaving the remaining 4th order terms to 2nd order terms, yielding the scheme 2nd order accurate.

Hope this makes sense :)