Finite Difference Method (challenging)

[Amanv]

Hey,


So i have a lengthy assignment which i am trying to make my way through. Below there are attachments for the assignment and my attempt at task 1.


Now i thought i was on the right track, using the finite difference method to approximate the 2nd order derivatives and using the formula to form a matrix...however, i went to see my lecturer (who isn't very useful) and apparently i have to write it in the nth term? I cant seem to get my head around this as my maths isn't the best. Could someone please explain how to work out to the nth term and advise me on task 1? =]

Thank you,

Aman Varma

 

[Deleted member 4993]

Hey,


So i have a lengthy assignment which i am trying to make my way through. Below there are attachments for the assignment and my attempt at task 1.


Now i thought i was on the right track, using the finite difference method to approximate the 2nd order derivatives and using the formula to form a matrix...however, i went to see my lecturer (who isn't very useful) and apparently i have to write it in the nth term? I cant seem to get my head around this as my maths isn't the best. Could someone please explain how to work out to the nth term and advise me on task 1? =]

Thank you,

Aman Varma


View attachment 5079View attachment 5080View attachment 5081View attachment 5082View attachment 5083View attachment 5084

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

 

[Amanv]

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

I have posted pictures of my work already, although im not sure if this is correct or not.
personally i think that the matix formed at the end needs to be a general matrix which could be applied to any point within the reservoir/cube. I think this because we havent been given the dimensions. On the 2nd page of the assignment towards the bottom half of the page it is written...:

pressure at t = 0 s from element 1 to element (n? 1) is constant and equal
to the pressure Pn in the last block n , where n = 0; 1; 2; : : : ; n in all three
dimensions

Im not really sure what this means but am assuming this has some importance....

 

[Amanv]

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

I have taken pictures of my work and submitted it within the original post, does anyone know if this is the correct approach to take? I think that i have to create a general matrix where any point within the cube/reservoir can be mapped?

Also in the 2nd page of the assignment, the following statement is written towards the bottom of the page:

pressure at t = 0 s from element 1 to element (n? 1) is constant and equal
to the pressure Pn in the last block n , where n = 0; 1; 2; : : : ; n in all three
dimensions

Unfortunatley i am not really sure on what this actually means, however i am thinking this will help me derive a general matrix for an Nth term?