# Finite difference problem

• Mar 14th 2014, 08:09 AM
Vinod
Finite difference problem
Hi,
Here is problem:

Given that $u_x$ is a polynomial of second degree and $u_0=1,u_1+u_2=10,u_3+u_4+u_5=65$

Find the value of $u_{10}$
Solution:
Now, here how should I make sub-division of intervals? i-e suppose we are given every nth value of a function and it is required to find out the values of the function at the

individual points. e.g., the quinquennial values $u_0,u_5,u_{10},u_{15},.....$ or decennial values $u_0,u_{10},u_{20},u_{30},....$are known and it is required to complete the

series $u_0,u_1,u_2,u_3,.....$ we can calculate $\delta u_x, \delta u_x^2, \delta u_x^3$ and so on
Any hint to solve this problem is appreciated.
• Mar 14th 2014, 08:20 AM
romsek
Re: Finite difference problem
Quote:

Originally Posted by Vinod
Hi,
Here is problem:

Given that $u_x$ is a polynomial of second degree and $u_0=1,u_1+u_2=10,u_3+u_4+u_5=65$

Find the value of $u_{10}$
Solution:
Now, here how should I make sub-division of intervals? i-e suppose we are given every nth value of a function and it is required to find out the values of the function at the

individual points. e.g., the quinquennial values $u_0,u_5,u_{10},u_{15},.....$ or decennial values $u_0,u_{10},u_{20},u_{30},....$are known and it is required to complete the

series $u_0,u_1,u_2,u_3,.....$ we can calculate $\delta u_x, \delta u_x^2, \delta u_x^3$ and so on
Any hint to solve this problem is appreciated.

I'm not really sure what you are asking here. You have a 2nd order polynomial, i.e. 3 parameters, and a system of 3 equations. Simply solve for your parameters and use them to evaluate $u_{10}$

I get

Spoiler:
$f(x)=x^2+x+1~~~~u_{10}=f(10)=111$

What am I not understanding?
• Mar 14th 2014, 09:41 PM
Vinod
Re: Finite difference problem
Hi Romsek,