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.

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

What am I not understanding?

Re: Finite difference problem

Hi Romsek,

I got answer to the problem.Your reply was helpful.