Finite difference method; finding the 'Stencil'

[the_dane]

Homework Statement

Determine the Finite Difference Method stencil for approximating a second derivative u''(x) at a discrete set of nodes with maximum accuracy for stencil of sizes (0,4) (off-centered).

My questions:
I think I am able to answer the question I am just not sure about what is asked about. First of all, what is a FDM stencil? The way I understand it the stencils is the five points (a+h*0), (a+h*1) (a+h*2), ... and (a+h*4), where the approximation is centered around a. Am I correct?

What is ment with "maximum accuracy".

Homework Equations

The standard equations for Finite difference method

The Attempt at a Solution

To be honest I have not made any attempt yet because, as mentioned above, I am not sure what I am asked about

 

[tnich]

Homework Statement

Determine the Finite Difference Method stencil for approximating a second derivative u''(x) at a discrete set of nodes with maximum accuracy for stencil of sizes (0,4) (off-centered).

My questions:
I think I am able to answer the question I am just not sure about what is asked about. First of all, what is a FDM stencil? The way I understand it the stencils is the five points (a+h*0), (a+h*1) (a+h*2), ... and (a+h*4), where the approximation is centered around a. Am I correct?

What is ment with "maximum accuracy".

Homework Equations

The standard equations for Finite difference method

The Attempt at a Solution

To be honest I have not made any attempt yet because, as mentioned above, I am not sure what I am asked about

You have given us nothing to work with here. It looks like you need to do some reading to understand the terminology used in the problem statement. Please do that and then make an attempt at a solution. Then we might be able to help you.

 

[the_dane]

You have given us nothing to work with here. It looks like you need to do some reading to understand the terminology used in the problem statement. Please do that and then make an attempt at a solution. Then we might be able to help you.

You're right that I am not quite certain about there terminology. I am using the textbook by Levee: Finite Difference Methods for Ordinary and Partial DE.

But the terminology is not clear for me and that is Exactly what I am asking about. My answer to the question is: (a+h*0), (a+h*1), ... and (a+h*4).

Basically what I want is that someone tell me why I am right or wrong.

 

[tnich]

You're right that I am not quite certain about there terminology. I am using the textbook by Levee: Finite Difference Methods for Ordinary and Partial DE.

But the terminology is not clear for me and that is Exactly what I am asking about. My answer to the question is: (a+h*0), (a+h*1), ... and (a+h*4).

Basically what I want is that someone tell me why I am right or wrong.

So you are giving us a guess based on almost-but-not-quite nothing. When your textbook has explained something in a way that you do not understand, it is helpful to look at other books until you find an explanation you do understand.
Are you points centered around $a$?

 

[Stephen Tashi]

I am using the textbook by Levee: Finite Difference Methods for Ordinary and Partial DE.

I can't find that book listed anywhere. What is the author's full name?

 

[tnich]

I can't find that book listed anywhere. What is the author's full name?

Is it this book by Leveque? http://epubs.siam.org/doi/abs/10.1137/1.9780898717839.ch1