TS Approx of Second Derivative

I think I might be on the track of this one.

Step 1. Follow text book's approach to solving for f'(x) Keep that result for later.

Step 2. Produce the right Taylor Series (which might be difficult to see straight off) to solve for f''.

Step 3. Do that. Get f'' out of that TS and on its own side of the equation.

I think before the manipulations is the time to plug in the f' expression you got in Step 1. Whatever. Plug it in at an appropriate time so that the entire other side expression is in terms of f and h.

Somehow or other that first error term falls away? Or do we have to keep an additional f'' term in the error? We certainly can't just simply wish it away.

There ought to be an f''' term for error.

Now one of the problems is that unless you simply know the formula you must solve for (and they're not all in the text book) how would you know whether you're working with forward, backward, or central approximations?

I don't intend investing too vast an amount of the little time left on this, but how does the general scheme of it sound?

Ja. You lost me at Step 2. I've mailed the lecturer about this question. Lets wait and see. I will call this afternoon again - she was in a meeting this am apparently.

Step 2's right TS would be chosen from among Forward, Backward, and Central differences.

Your f'' approximation would also be characterised as one of these (forward etc).

In other words you would probably not get the desired result if the formula to reach was a central difference formula for f'', but you put a backward differences approximation of f' into it when you solved.

Step 3 could be rephrased as "isolate just f'' on the LHS of the equation, and move all other terms to the RHS".

f'' = (OldRHS - TermsThatOnceWereAddedToF2prime) / FactorsOfF2prime