1. ## Checking Taylor Expansions

Hi, I just want to check that I have the Taylor expansions correct for these choices.
I cannot find any examples on the net. So would be great if you could give me these.
$y(x_{i+1})$
$y(x_{i+2})$
$y'(x_{i-2})$
$y'(x_{i+1})$

2. I think we're missing an awful lot of information here. What is $y?$ Where are your $x_{i}$'s?

3. Originally Posted by james12
Hi, I just want to check that I have the Taylor expansions correct for these choices.
I cannot find any examples on the net. So would be great if you could give me these.
$y(x_{i+1})$
$y(x_{i+2})$
$y'(x_{i-2})$
$y'(x_{i+1})$

CB

4. Originally Posted by Ackbeet
I think we're missing an awful lot of information here. What is $y?$ Where are your $x_{i}$'s?
Hi, for example a solution could be:
$y(x_{i+1})=y(x_{i})+hf'(x_{i})+((h^2)/2!)*f''(x_{i})$ (not sure if this is correct)
where $h=x_{i}-x_{i-1}$ and $x_{i}$ is a general point.

Thanks
James

5. Ok, so it looks like you're trying to construct an iterative sequence out of the Taylor series expansion for a function. Is that correct? If so, where do you want to expand the Taylor series? It matters where you're trying to expand the series.

6. Originally Posted by Ackbeet
Ok, so it looks like you're trying to construct an iterative sequence out of the Taylor series expansion for a function. Is that correct? If so, where do you want to expand the Taylor series? It matters where you're trying to expand the series.
The actual question I am asked is:
Find the principle local truncation error and the order of Quade's method
$y_{n+1}-8/19*(y_{n}-y_{n-2})-Y_{n-3}=6/19*h*(y'_{n+1}+4y'_{n}+4y'_{n-2}+y'_{n-3})$

And the idea is to use the Taylor series and cancel out to get the error. So I assume it is around x=0.

Thanks
James

1. I assume the last term on the LHS is meant to be lower-case.

2. In googling Quade's method (which I've never heard of before), I saw at least one definition of it that has different indices than yours. Here's one such example. I don't know if it's correct or not. There seem to be multiple definitions of the method out there.

I'm out of my league here. CB, what do you think?